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Hauk, M. (2013, May 1). Five fractal geometries for creative, sustainable, and just educational design. Paper presented at the 2013 annual meeting of the American Educational Research Association (AERA). Conference Theme: “Education and Poverty.” San Francisco, CA. Interactive Symposium, “The Geometries of Liberation: The Hidden Wealth of Patterns and Materials Outside the Grid,” for Division B, Curriculum Studies, Section 4: Sustainability, Environmental, and Ecological Perspectives.

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Abstract and Figures

This research concerns the use of fractal patterns to spark group creative collaboration for sustainability education design. Fractal patterns in nature can serve as templates or archetypes for innovative social structures and processes, addressing the poverties of reductionism in education itself. This paper focuses on five “ecofractal” fractal geometries. Small group mixed-methods research with higher educational research designers over a two-year period, using five fractal geometries as prompts, produced innovative educational research systems design. In both divergent and convergent creative production, the vortex, radiance, hive (packing), branching, and flow patterns produced innovation to liberate learners and learning systems. Further qualitative research with groups of adult learners (including community poets using poetic inquiry) extended findings and theorizing in how these geometries of liberation, grounded in examples from nature and bioculture, can provide meaningful interventions in course content, classroom setup, experiential immersion, design of educational research systems, community project and service learning, and critical pedagogies. A Transdisciplinary Regenerativity Index was developed by synthesizing theorists’ work on regenerative design across fields and used as an assessment tool for group work. In this research, use of these geometries of liberation was shown to significantly increase participants feeling more creative, hopeful, inspired, and connected. Additionally, examples emerged of effective collaborative learning and enhanced learner ethics and ecojustice/ anti-domination thinking. These ecofractal geometries hold promise to see differently and take inspiration from what is abundantly available, to liberate groups of learners to generate more regenerative gardens, classrooms, research, and school systems, for ethics and justice.
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Paper Title
Five Fractal Geometries for Creative, Sustainable,
and Just Educational Design
Marna Hauk, Institute for Earth Regenerative
Studies and Prescott College
Author(s)
Geometries of Liberation: The Hidden Wealth of
Patterns and Materials Outside the Grid
Session Title
Session Paper
5/1/2013
Presentation Date
San Francisco, California
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Descriptors
Methodology
Division B - Curriculum Studies
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Five Fractal Geometries for Creative, Sustainable, and Just Educational Design
As part of the
Geometries of Liberation Interactive Symposium
American Educational Research Association (AERA) 2013 –
Education and Poverty: Theory, Research, Policy, and Praxis
Marna Hauk
PhD Candidate, Sustainability Education
Graduate Faculty
Prescott College
Prescott, Arizona
Institute for Earth Regenerative Studies
Portland, Oregon – Pacific Cascadia Bioregion
PO Box 14194
Portland, Oregon 97293
earthregenerative@gmail.com
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FIVE FRACTAL GEOMETRIES FOR CREATIVE, SUSTAINABLE, JUST EDUCATION
2
Abstract
This research concerns the use of fractal patterns to spark group creative collaboration for
sustainability education design. Fractal patterns in nature can serve as templates or archetypes for
innovative social structures and processes, addressing the poverties of reductionism in education
itself. This paper focuses on five “ecofractal” fractal geometries. Small group mixed-methods
research with higher educational research designers over a two-year period, using five fractal
geometries as prompts, produced innovative educational research systems design. In both
divergent and convergent creative production, the vortex, radiance, hive (packing), branching,
and flow patterns produced innovation to liberate learners and learning systems. Further
qualitative research with groups of adult learners (including community poets using poetic
inquiry) extended findings and theorizing in how these geometries of liberation, grounded in
examples from nature and bioculture, can provide meaningful interventions in course content,
classroom setup, experiential immersion, design of educational research systems, community
project and service learning, and critical pedagogies. A Transdisciplinary Regenerativity Index
was developed by synthesizing theorists’ work on regenerative design across fields and used as
an assessment tool for group work. In this research, use of these geometries of liberation was
shown to significantly increase participants feeling more creative, hopeful, inspired, and
connected. Additionally, examples emerged of effective collaborative learning and enhanced
learner ethics and ecojustice/ anti-domination thinking. These ecofractal geometries hold
promise to see differently and take inspiration from what is abundantly available, to liberate
groups of learners to generate more regenerative gardens, classrooms, research, and school
systems, for ethics and justice.
Keywords: education, sustainability education, transdisciplinarity, regenerativity,
ecofractal, fractals, geometry, creativity, diversity, liberation
FIVE FRACTAL GEOMETRIES FOR CREATIVE, SUSTAINABLE, JUST EDUCATION
3
Introduction
Using complexity and chaos frames to design novel research in group creative
collaboration, I hoped to discover if natural patterns can catalyze creativity, justice, and
regenerativity (beyond sustainability) in learning systems.
This research is part of a larger body of doctoral scholarship still in flight spanning
multiple scales. Within the scale of group collaboration, the larger body of research includes five
encounter sites of natural pattern (ecofractal) educational research. This paper touches on two of
these five sites of ecofractal encounter.
In the first of these two sites described, a group of faculty educational researchers met
over a two-year period (2011-2012) using ecofractal-style prompts to catalyze their redesign of
college-wide research ethics review. This engagement occurred at a time when their college was
refocusing on an environmental and social justice mission and investing in increasing support for
student and faculty research.
The second site of ecofractal encounter featured in this symposium paper was a two-
evening workshop called “The Great Tapestry.” The research workshop was held for community
poets in collaboration with the Institute for Poetic Medicine and featured individual and group
processes sparked by five ecofractals in September 2012 in Portland, Oregon.
In the larger body of research, the ecofractal work is evaluated using a mixed methods
approach, including four quantitative evaluations as well as two qualitative approaches,
including assessments at the scale of the individual participant as well as assessments at the
group/emergent scale. This paper highlights initial findings from three of these six arenas.
FIVE FRACTAL GEOMETRIES FOR CREATIVE, SUSTAINABLE, JUST EDUCATION
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In order to understand how the living planet models regenerative processes, I surfaced
and refine a set of process-patterns that weave through nature and bioculture and with which
nature weaves. Because these patterns are ecological and fractal across scales, I use the
shorthand term “ecofractal” to denote them. Ward (2010) emphasizes that, for ecological
education, “careful observation and natural pattern mimicry are the all-encompassing skills”
(section 4, para. 4).
Several research design considerations apply to this research concerning ecofractals. My
research to date in this field (including Hauk, 2011) has emphasized the need that the ecofractals
be treated as processual (honoring their arising as processes rather than becoming fixed or
iconic) and that they are dynamic rather than static. Within the paradoxes of complex
adaptive/living systems, ecofractals are self-similar patterns that continue to emerge. The energy
flowing through the form is what is creating the form and is of at least as much interest, rather
than focusing merely on the husk or shape of the flow. Finally, I committed in this work to
increase researcher and participant embedment within these process-patterns from nature
(including bioculture). Ecofractals are not simply objects to look at and perceive or utilize in a
Cartesian illusion of separation. I continue to effort to embed and embody and immerse the
research within these living patterns rather than scrutinize or reduce them.1
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1 Savvy complexivists will question the use of terms such as “outcomes” and “work products”
and the word “productive” in this research reporting. I am open to continuing insight and
conversation regarding how to conceptualize and synthesize this work within living systems
approaches and thank you in advance for your help, insight, and collaboration in this process.
Note here too that the emphasis on emergence, process orientation, and embedding and
embodying gives kinship between this research and Gaian methods approaches (see
deChambeau, Hauk, & Landsman, 2010; Hauk, Landsman, Caniglia & Canty, 2010).
FIVE FRACTAL GEOMETRIES FOR CREATIVE, SUSTAINABLE, JUST EDUCATION
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Literature Review
My research concerns the use of fractal patterns to spark group creative collaboration for
sustainability education design. Relevant literature in this endeavor includes (1) the rich research
on fractals and divergent creative production, (2) the body of scholarship exploring fractal
patterns and educational system innovation for justice and complexity as a theory for education,
as well as (3) the research in creativity around collaborative emergence.
Fractals and Divergent Creativity in Education
Fractals have been shown to catalyze and model the process of divergent creativity
(Richards, 2001a, 2001b, 2007, 2010; Sterling, 2003). Fractal patterns in nature can serve as
templates or archetypes for innovative social structures and processes, addressing the poverties
of reductionism in education itself. Goldstein, Hazy and Lichtenstein (2010) argue for generating
ecologies of innovation leveraging chaotic patterns, furthering insights regarding fractal
innovation (Capra, 2002; Ball 1999, 2012). Fractal geometries are –and produce learning that
is—proliferative and multiple rather than singular and deterministic: from a seed or kernel
pattern, with elaborations of elaborations resulting “in an endless, recursive, ever-complexifying
process like the ones that eventually give rise to the scale independence of fractal images,” with
applications for educational practice (Davis, Sumara & Luce-Kapler, 2008).
Fractal Patterns and Educational System Innovation for Justice
Fractal patterns can support innovative design in educational systems (Hauk, 2011).
Research in the sustainability education field leverages natural pattern, chaos, and critiques of
reductive grid patterning, including fractal geometries of liberation (Sterling, 2001; Nolet, 2009;
Díaz, 2010). Applications include sustainable activism with inner city gardens at the intersection
of art and nature (Boggs & Kurashige, 2011). They produce justice alignment and solidarity
FIVE FRACTAL GEOMETRIES FOR CREATIVE, SUSTAINABLE, JUST EDUCATION
6
(Bowers, 2011; Funtowicz & Ravetz, 2008) against dogmatism and for liberation of the
oppressed (Ambrose & Sternberg, 2012; Ráez-Luna, 2008). They highlight the “e” of equity in
the triple e’s of sustainability (equity, ecology, and economics). And, similar to biological and
ecological examples sparking design innovation in biomimicry (Benyus, 2002) and regenerative
design (Van der Ryn & Cowan, 2007; Lyle, 1994), fractal geometries can spark creative
production for just and ethical educational design and delivery.
Research orientation – Complexity Education and Convergent Collaborative Creativity
Congruent with complexity as an educational theory, this research resonates with the four
conditions for emergence in educational collectivities, including internal diversity, internal
redundancy, (density and depth of) neighbor interactions, and decentralized control (Davis &
Sumara, 2008, p. 38). The improvisational and spontaneous nature of the experiences fits this
research within the collaborative creative emergence theorizing of Sawyer (2010, 2012).
This work orients itself from within a complexivist frame. I could take as the research
orientation and aim a capable description of the transphenomenal, transdisciplinary,
interdiscursive power of complexity and living systems approaches. Davis and Sumara (2008)
describe how “complexity thinking [is] emphasizing the need to study phenomena at the levels of
their emergence, oriented by the realization that new stable patterns of activity arise that are
specific to the emergent system” (p. 36).
Across dimensions of social creativity, aligning with Kurtberg and Amabile’s (2001)
affirming the need for creativity research in the arenas of group creativity as “the next horizon: to
expand the scope of this field and explore creativity in all of its manifestations, from single
individuals working together, to small teams, to large and complex groups” (p. 292). Group
creative collaboration has been differently understood as social or by function (Batey &
FIVE FRACTAL GEOMETRIES FOR CREATIVE, SUSTAINABLE, JUST EDUCATION
7
Furnham, 2006; Kozbelt, Beghetto & Runco, 2010), and the field of creativity continues to
reorient beyond the elite solo genius conception (Montuori & Purser, 1995). The work of several
scholars researches insect collectives and complex intelligences for patterns of creative
emergence (Sulis, 2009, 2011; Wisdom & Goldstone, 2011).
Sawyer (2010, 2012) affirms this approach. He has developed a creativity framework of
collaborative emergence particularly relevant for effects in the current research (also Sawyer &
DeZutter, 2009). Sawyer’s “framework of collaborative emergence can be used to determine the
relative benefits of individual-level explanations and group-level explanation when examining
any specific case of creativity” (2010, p. 365). He argues “the best scientific explanation of
creativity will involve multiple levels of analysis. They will incorporate properties and laws
associated with individual and with groups” (p. 367). Sawyer’s collaborative emergence
framework is an affirmation of the creativity approach used in the current work, which includes
detailed examination of both individual and group scale effects of creative collaboration,
including studying an emergent phenomenon, regenerativity.
Methods
Overview
This presentation focuses on five “ecofractal” fractal geometries. Small group qualitative
research with higher educational research designers over a two-year period used ecofractal
approaches and prompts to innovate educational research systems design. Further work with a
group of community poets in a two-day intensive explored each of these five fractal geometries.
The groups used both divergent and convergent creative production sparked by the vortex,
radiance, hive (packing), branching, and flow patterns. This ontology of ecofractal patterns in
nature is an adaptation of Murphy, Neill and Ackerman (1993).
FIVE FRACTAL GEOMETRIES FOR CREATIVE, SUSTAINABLE, JUST EDUCATION
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The group work products were evaluated using the Transdisciplinary Regenerativity
Index (Hauk, 2013). This Regenerativity Index was developed by synthesizing many theorists’
work on regenerative design across fields and used as an assessment tool for group work.
General Methods
Complexity education approaches involve creating conditions for learning emergence
(Davis & Sumara, 2006, 2008). These conditions enable activating catalysts to serve as system
perturbations. An activating catalyst could include, for example [for Group 2], a brainstorm
sparked by words picked at random from the dictionary, global challenges such as industrial-
growth society, hunger, or climate change, a poem, a branch, group art-making with words cut
from poems, medicinal herbs harvested from the garden, and physically created nonlinear shapes
within shapes (a spiral laid out on the floor with fabric, with stations such as a shell, a dragon
sculpture, a bell as prompts). As a (complex/living/learning) system becomes perturbed, self-
organization can occur. The students and teachers then are together generating what Bache
(2008) has characterized as “living classrooms.” The teacher moves from controlling learning to
(co-) creating conditions and designing perturbations for educational emergence to come to life.
The design of these ecofractal research interventions did feature the key “conditions that
must be in place to allow the emergence of such expansive possibilities” including internal
diversity, internal redundancy, depth and density of neighbor interactions, and decentralized
control (Davis & Sumara, 2008, p. 38, mentioned above). A variety of contexts were generated
to experiment with how to expand the internal diversity and harvest internal similarity along with
optimizing depth and density of neighbor interactions, all within a context of decentralized
control and intense spaciousness for self-organizing (autopoietic) emergence.
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To note, this research, and the larger research project of which it is a part are framed
within a Gaian methodologies orientation. The embedment of researchers and participants within
the research system, the processual and complexivist nature of the work, the attention to
emergent effects (including the planetary and regenerative) including the action of the research
itself catalyzing autopoiesis all bring it into the purview of a Gaian research lens (deChambeau,
Hauk, Landsman, 2010; Caniglia, Canty, Hauk, Landsman, 2010; Hauk, 2013).&
Methods – Group 1
Longitudinal Study with Regenerative Approaches (2 intensives) - Examples of Regenerative
Educational Design Using Complex Living Systems and Ecofractals
One ecofractal longitudinal study involved working with a faculty committee at a small
Eco-League college who was tasked by the full faculty to redesign the institutional review and
research support processes for the College. Two day-long design intensives and twice-monthly
touch point sessions were opportunities to innovate in small group creative collaborations. Each
of the day-long design retreats included different approaches to catalyze divergent production.
Group 1 – Session 1 - Institutional Review Board Complex Living Systems Design Intensive –
January 2011 [Session 1]
In Retreat 1 (January 2011), general background and prompts regarding four complex
living systems design approaches drove design, including: (1) complex adaptive systems, (2)
biomimicry, (3) ecological systems and ecological models, and (4) symbiogenesis. Additionally,
the team was offered background reading in complexity and research design (Mason, 2008),
regarding the conditions for complex emergence (Davis and Sumara, 2006), and regarding
complexity and knowing frames (Davis, Sumara, & Luce-Kapler, 2008), as well as orientation to
examples of biomimicry (Benyus, 2002; Biomimicry Group, 2011) and ecological design models
FIVE FRACTAL GEOMETRIES FOR CREATIVE, SUSTAINABLE, JUST EDUCATION
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(e.g., Mollison, 1990). Symbiogenesis was another group prompt. Symbiogenesis is a concept
popularized by Lynn Margulis (1998) – detailing how different living forms affiliate together to
generate more complex life forms. This concept provided a rich source of creative productivity,
highlights aspects of collaboration in natural systems and evolution.
Note, all of these approaches have kinship with the evolving ecofractal approaches in the
larger research. The qualitative research question between the two sessions was, what are
effective ways of supporting group creative collaboration? What would the results be from
introducing looser, whole-concept/ approach introductions (e.g., biomimicry, ecological design,
symbiogenesis) as compared with a specific natural pattern focus (e.g., packing/beehive,
vortex/hurricane, etc.)?
Group 1 – Session 2 - Institutional Review Board Ecofractal Design Intensive – January 2012
The second, full-day design intensive applying research two was held a year later,
January 17, 2012.
Ecofractal Prototype Cards. Group 1, Session 2 utilized prototypes of ecofractal cards
(words on 1/16th pieces of paper), including each pattern as itself, and as processes, relationships,
and actions, with directionality across them. For example, for the ecofractal of packing, cards
included: Pattern: Honeycomb/Pomegranate; Process: [Generated from the Group] Beehive.
Relationship cards included Diverge, Weave Together, Jump Scales, and Collaborate, etc.
Actions cards included: Nurture, Perceive, Close/ Open, Subsume/ Surround, Aggravate,
Collaborate, etc. Directionality could include Convergent, Divergent, and Crazed. [This group
used early prototypes; the cards are currently (April 2013) on their sixth iteration.] The group
assembled a space central to the day’s work with objects emblematic or evocative of each of the
ecofractals (e.g., a bird nest for radiance; strands of horse hair for flow) and spent time
FIVE FRACTAL GEOMETRIES FOR CREATIVE, SUSTAINABLE, JUST EDUCATION
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connecting with and discussing different objects and how they could relate to and represent
regenerative systems. The group used the ecofractals in divergent and convergent design of their
major challenges, including how to catalyze and nurture a research culture of collaboration that
was self-organizing and self-sustaining, and how to educate for and cultivate ethical
consideration of living systems in research design.
Methods – Group 2
In contrast to the longitudinal approach of Group 1, who met over two years, Group 2
was a spontaneous assemblage of community poets focused on ecofractal patterns. Poetic inquiry
was one of the additional methods used for Group 2 research. Poetic inquiry methods include
using poems as educational prompts as well as the creation of poetry as a qualitative research
response (Prendergast, 2009; Prendergast, Leggo, & Sameshima, 2009). Poetic inquiry offers
relevant methods for exploring the intersection of the imaginal and the phenomenal; in particular,
poetry is complex and dense enough to support the articulation of systems level emergence.
The group convened and met for two evenings, two hours each evening, to explore
ecofractals and regenerative creativity in September 2012, on the topic “The Great Tapestry.”
John Fox from the Institute for Poetic Medicine kindly co-facilitated the poem-making portions
of the event. The two evenings of workshop encounter, “The Great Tapestry,” were sparked by
one of Rilke’s Sonnets to Orpheus, Part II, Number XXI, which describes a voluptuous sensory
walk through fantastical gardens, and, speaking of the senses and images experienced, ends with
these lines:
Like a silken thread, you entered the weaving.
Whatever image you take within you deeply,
even for a moment in a lifetime of pain,
see how it reveals the whole--the great tapestry.
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(Rilke, Translated by Barrows & Macy, 2005, p. 127)
This poem touches on the research themes of embedment, ecological pattern, autopoiesis,
creativity, and regeneration.
The ecofractal research in “The Great Tapestry” was catalyzed according to research
protocols intended to diversify the intersection of ecofractal pattern and technique(s) of
exploration. Each of the prompts or raw materials provided was considered a perturbation for
creative synergy and emergence. For example, branching prompts included an actual large
branch (of sage, wormwood, fennel, mugwort, etc.) handed to each participant. Radiance was
explored by small collaborative groups building nests from poem words, twigs, and yarn. Flow
was explored through overnight poem-making “homework” sparked by flow poems (e.g.,
Older’s “River O River” and Martha Graham “On Creativity”). Work with the pattern of
packing involved poem-making in a silent circle, with participants encountering whole-sheet
images (examples of packing) and then writing for one-minute per image, then passing the
images clockwise. Vortex exploration involved interacting with physical objects placed at
stations on a spiral-shaped ground cloth, with participants spiraling in (or out) from station to
station, responding for one minute per
prompt station. (See Appendix 2 for more
detailed listing of poems used).
Ecofractal cards. The final group
process involved a group “poemstorm”
utilizing version 5 of the ecofractal cards,
each one-ninth of an 8 ½ x 11 piece of
Figure 1 Ecofractal Card Example, "Spiral Galaxy -
Vortex" – Hauk, 2012
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13
paper. The version 5 set included divergent and convergent pattern for each ecofractal, featuring
a specific pattern example visualized by a Wikimedia Commons or public domain image. Each
pattern card also included emergent themes, associations, and concepts. The relationship and
action cards were similar to those used in prototype 1 of the card set, made larger, text on paper.
(See Figure 1 for example ecofractal pattern card. Detailed research protocols and example cards
are included in the larger body of the dissertation work.)
Evaluation Methods
Since the aim of the research was to create conditions that would catalyze educational
emergence, this research included both individual and group assessments (starting in mid-2011).
Creativity can be a difficult thing to assess (Hargreaves & Bolton, 1972). Guastello and Fleener
(2011) note how the surprise and suddenness of creative processes make them relevant
candidates for nonlinear research approaches (p. 143), and chaotic patterns underlying creativity
are the topic of several research studies (e.g., Sterling, 2003, and Richards, as noted above).
Two tests of individual creativity were administered as part of the larger research. For
ease, the individual creativity instrument administered was the paper and pencil Guilford
Alternate Uses Task, which can take a pulse on the flexibility, fluency, originality, and
elaboration of individual divergent creative production (Guilford, Christensen, Merrifield, &
Wilson, 1978; Bonk, 2003). Secondly, I developed an instrument for the individual participant
administered directly preceding the Alternate Uses Task, with an acronym of the “CHIC” –
which offers a Likert-style self-evaluation at a point in time across four dimensions, “how
creative/ hopeful/ inspired/ connected” does the participant feel. Each of these was administered
before and after the experiences. Analysis of individual creativity via the Guilford Alternate Uses
FIVE FRACTAL GEOMETRIES FOR CREATIVE, SUSTAINABLE, JUST EDUCATION
14
Taskis part of the larger dissertation work. This paper focuses individual creativity reporting on
the results of the second, “CHIC” instrument.
Importantly, the research also needed to gauge group effects. Two instruments were used.
After each experience, participants shared brief self-reflections on the group experience. Lastly,
for the larger body of my research within which this scale of research resides, I prototyped a
more extensive tool for group process/system emergence and work product assessment, a
Transdisciplinary Regenerativity Index (Hauk, 2013). Rather than raw count of ideas produced in
brainstorming as a metric of divergent production (Paulus & Brown, 2003), complex and living
systems approaches would suggest that the regenerativity of the ideas is important. The
Transdisciplinary Regenerativity Index (or TRI or Regendex), currently under development as
part of the larger research project, looks within and across disciplines for attributes, factors,
conditions, indications, and descriptions of regenerativity. Regenerativity is conceived here as a
type of emergent creativity, a kind of self-organizing autopoiesis beyond sustainability,
particularly appropriate for group and systems scales. A prototype of the TRI/Regendex sourced
from transdisciplinary sources was utilized to assess group work products. The larger body of
research is ongoing and, due to space limitations in this context, initial and brief descriptions of
findings are shared here.
Further, several qualitative views across the findings and work emerging from the
experiences are shared below. These include rich tapestries of poetic response oriented around
each ecofractal, as well as descriptions of some visual brainstorm artifacts. I discuss the potential
meanings of these designs and ecofractals as geometries of liberation.
Findings
In both divergent and convergent creative production, the vortex, radiance, hive
FIVE FRACTAL GEOMETRIES FOR CREATIVE, SUSTAINABLE, JUST EDUCATION
15
(packing), branching, and flow patterns produced innovation to liberate learners and learning
systems.
Further qualitative research with groups of adult learners extended findings and
theorizing in how these geometries of liberation, grounded in examples from nature and
bioculture, can provide meaningful interventions in course content, classroom setup, experiential
immersion, design of educational research systems, community project and service learning, and
critical pedagogies. In this research, use of these geometries of liberation was shown through
pre- and post-testing to influence creativity along dimensions of fluency, flexibility, originality,
and elaboration. Other positive effects surfaced in the research such as effective collaborative
learning and enhanced learner ethics and ecojustice/anti-domination thinking. Fractal geometries
hold promise to see differently and take inspiration from what is abundantly available, to liberate
groups of learners to generate more regenerative gardens, classrooms, research, and school
systems, for ethics and justice.
Creative Collaborative Emergence – Highlights - Ecofractal-Infused Designs
One question of this research has been, will infusing ecofractal and ecological (and
biocultural) pattern processes and concepts into group collaborative design yield more
regenerative designs? “The Great Tapestry” research workshop produced three group work
products, one was a shared “po” (DeBono, 1985)-possibility inspired brainstorm that riffed on
the juxtaposition of “random” prompts for a common purpose. Additionally, participants broke
into triads for the radiance ecofractal pattern exploration, building physical “nests” inspired by
the patterns of radiance. A final activity for the whole group involved using the ecofractal cards
in a group brainstorm regarding novel cultures of creative liberation (Iteration 6 of the cards
were used). All these group work products were assessed using “Iteration 1” (a simplified form)
FIVE FRACTAL GEOMETRIES FOR CREATIVE, SUSTAINABLE, JUST EDUCATION
16
of this researcher’s Transdisciplinary Regenerativity Index. Group 1 (the Research Process
design team, longitudinal study) also surfaced several creative collaboration designs, both by
general prompt and specific collaboration experiments with ecofractal patterns. The following
table shares highlights of the outcomes for group work products.
Table 1
Group 1 and 2, Context Details and Highlights of Work by Group
Group
Group 1
Group 2
Details
Group 1
Session 1
January 2011
Group 1
Session 2
January 2012
Group 2
Sessions 1 & 2
September 2012
Context
College faculty
College faculty
Community poets
Type
Longitudinal, already convened for another
purpose
Single Instance
Duration
6 hours, 1 day
6 hours, 1 day
4 hours over 2 days
Group Work 1
Brainstorm Process
Redesign
Research “Nest”
Design
“Po” Brainstorm -
Panegyric
Examples/
Keywords
Using river filtration as a
model for proposal
process. The system
should learn from itself,
earlier vetting “upstream
through peer and faculty
review and the support of
“Research roundtables”
cleanses the proposal
stream by the time it
converges on the IRB and
flows through.
Using the pattern of
radiance, create self-
organizing communities of
researchers who are
nurtured but also feel free
to “fly off” –increase
resources and create peer
collaborations and
supports, sparked by
common methods or
topics, across contexts
A poetry-positive culture
where humans deliver
social justice poems and
organic food to all. Large
cultural festivals. CEOs
dress as hummingbirds
and other species and
radically reorient;
companies dissolve into
local cooperatives.
Group Work 2
Developing teaching
materials, strategies,
and stories
Twenty Questions
Team 1 and 2
Radiance Nest
Building – Groups 1-3
Examples/
Keywords
Ideas on how to create a
positive culture of
research, which generates
more of itself and feels
“alive”
Developed a college-wide
instrument for self-
reflection and initial
surfacing of assumptions,
bias, and limitations of
[Not conveyable in this
format.] Many riffed on
the line of Abram (2010),
“An eternity we thought
was elsewhere now calls
FIVE FRACTAL GEOMETRIES FOR CREATIVE, SUSTAINABLE, JUST EDUCATION
17
research design. Explicitly
includes considerations of
cultural and biocultural
appropriation and
consideration for living
systems in research ethics.
out to us from every cleft
in every stone, from every
cloud and clump of
dirt….”2 (2010, pp. 180-
181)
Group Work 3
Characteristics
Desired in the New
Process
Website Redesign
Final Harmonic
Ecofractal Card
Poem-making
Brainstorm
Examples/
Keywords
Developed a list of
characteristics desired in
the new process, including
promoting social justice,
anti-colonial, using
accessible and inclusive
language in which
researchers have an
understanding of the
abuses of research in the
past.
Developed a map of
information desired
including online videos,
collaboration space for a
research collaboratorium
(“the nest”), creating
multiple paths for different
learning styles and
allowing for growth and
change in the future
Webs of sanctuary of
stillness for poets and
creators from which
springs dervishing
community action to
increase sense of
connection, hug mobs for
inclusion, making space
for voices within the larger
incantations of life.
Group Findings
Findings, Group 1 – Session 1 (2011)
The first Institutional Review redesign process yielded fruitful and creative results.
Participants, sparked by prompts regarding regenerative design, collaboration and symbiosis, and
ecofractal patterns, emerged as a learning system and generated novel and just educational
designs.
Process. The group brainstormed using “po” (deBono, 1985) possibility prompt thinking
and ecofractal-oriented prompts. The exercises freed the group to draw from a wide range of
sources as inspiration. They leveraged biocultural insight to distinguish knowledge and wisdom
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
2&A fuller version of this passage from Abram (2010), “An eternity we thought was elsewhere now calls out to us
from every cleft in every stone, from every cloud and clump of dirt. To lend our ears to the dripping glaciers—to
come awake to the voices of the silence—is to be turned inside out, discovering to our astonishment that the
wholeness and holiness we'd been dreaming our way towards has been holding us all along…this animate immensity
that enfolds us, this spherical eternity, glimpsed at last in its unfathomable wholeness and complexity, in its
sensitivity and its sentience.” (2010, pp. 180-181)&
FIVE FRACTAL GEOMETRIES FOR CREATIVE, SUSTAINABLE, JUST EDUCATION
18
using the mythopoetic cycle of Odin who must lose sight in one eye (knowledge) to gain larger
vision (wisdom), to hang from the world tree in an immersive, surrendered state. They discussed,
for example, how unique turkey tail feathers that nevertheless created visual patterns could
provide insight on maintaining respect for unique variations while surfacing patterns in
qualitative research design.
Outcomes. The group was redesigning the institutional (ethical) review across four
college sub-populations. Sparked by ecofractal responses, they surfaced a model of living
systems considerations (including human-ecology embedment) and then mapped how to infuse
their future state design with living systems ethical considerations. They developed a process
model for (de)centralized ethical review of research that extended NIH concerns for “subjects” to
living systems as participants, including using cleansing river system ecologies as a process
model for vetting, reviewing, and filtering research proposals. This included modeling research
community contexts as active parts in the research proposal development process.
The team conceived of a set of questions for researchers to reflect on and surface
unconscious assumptions and positionality related to intersections of race, class, ethnicity,
orientation, species, and identity. Issues of consent were extended to the more than human world
and to increase awareness and designs avoiding appropriation of culture and species. One special
concern of the team was that college researchers not propound the grievous cultural harms done
in the name of research in relationship with First Nations people, lands, and cultures. Over time,
the team refined the “Twenty Questions” and it is now a part of the research process for all
research conducted in the College, still undergoing iteration and refinement.
Findings, Group 1, Session 2 (2012)
FIVE FRACTAL GEOMETRIES FOR CREATIVE, SUSTAINABLE, JUST EDUCATION
19
The second engagement with ecofractals for Group 1 convening on ethical research
design in higher education also proved fruitful. The group extended the “Research Round Table”
notion birthed in Session 1 into a “Research Nest” model to nurture research in the college,
envisioning cadres of faculty and student researchers self-organizing across programs via method
or topic combination. The team then used spatial and information architecture approaches to
collaboratively design the future website that would support this model as well as the stories and
content proliferation begun the year before. Outcomes also included refinements to the “Twenty
Questions” to deepen attention to the living systems and biocultural integrity approaches begun
in earlier work.
Findings Group 2 – The Great Tapestry (2012)
The treasure of “The Great Tapestry” was the opportunity to have a room of creatives
engage with the ecofractals and develop poetic understandings for each pattern. Branching
became a kind of reaching to connect as well as the roadmap of decisions toward clarity.
Liberation motifs relevant to this insight include the possibility spaces that the branching
ecofractal can open up creativity, self-determination, and reaching out to connect, which are very
useful in community organizing and service learning contexts. The ecofractal of radiance rang as
involving inclusion and belonging, able to catalyze liberation motifs of diversity, inclusion, and
community. Meandering flow’s immersion, empathy, and “yes” can nurture momentum,
(comradely) love, and affirmation. The proximity, closeness, and relationship in the pattern of
packing, such as in a beehive, could liberate closeness, safety, collaboration, sharing, and
resonance. And the change and transformation of the vortex, along with an emergent theme of
memory, can spin up revolution, integrity, and a sustaining justice. The tapestry of these
ecofractals in combination and emergence awakened harmony, scale jumping, embedment,
FIVE FRACTAL GEOMETRIES FOR CREATIVE, SUSTAINABLE, JUST EDUCATION
20
strengthening, and understanding in participants. These can offer coherence, connectedness,
drawing strength, and fluid nimbleness in complex systems as aspects of liberation to empower
learners, teachers, creative groups, and learning systems in biocultural thriving. (See Summary
Table below.)
Table 2
Overview of Poetic Descriptions and Liberation Motifs Per Ecofractal
Ecofractal
Pattern
With examples
Themes
from
Research
In Vivo Research Participant Sampler
Poem Excerpts (Detailed Credits in Appendix 1)
Liberation
Motifs
Branching
Tree branching
from trunk, bird
wings,
simplified “tree
of life”
evolutionary
taxonomy
depictions
Reaching out to
connect;
merging;
holding
difference,
making a
decision
“so I branch myself / out to be noticed / to hold and be
held, even to breaking” (JF, P11); “your velvet leaves /
reach up” (BD, P9); “If I knew you before / I only saw
today we are sisters / how you and I were plucked out /
from the earth and carried home” (CN, P2); “Come outside
now/ lean your back / against my sturdy self / see my
branches reaching / even down to you / out to light to air to
/ rain to fast squirrel” (P3); “the bit that reached deepest /
into the air. / It has already made friends with me / though
I do not know its name. / The life is still soft in it / in its
arching, leafing, flowering – / though it is broken / it seems
whole.” (P4); “see how each decided moment /by
movement to reach—the whole / spray is one hand as the
bush / is one hand of squillion deciding / fingers /
choosing to grow in that place / At the tip ends the fingers
spin / into a tender green question.” (DA, P5); “i would
rather join back down / to the mother trunk / flow back to
source, earthworm-haired /Gaia” (P12)
Reaching out to
connect
Curiosity
Self-determination
Decision making
and clarity
Radiance
Nova, ripples in
a pond, bud
burst, sitting
near a hearth
fire
Inclusion,
belonging,
community
“bound to those inside you, /held by those outside you”
(P10); “ripples forever on / the once quiet pond” (IS, P8);
“campfire / drawn together / around the life-giving
warmth” (P6); I can breathe deeply /again. /
harmonizing and belonging, / tucking in” (P12)
Diversity
Inclusion
Community
Flow
River meander,
circulatory
system,
migration
corridors
Immersion,
empathy /love
(interbeing),
saying yes,
drawing out/in
“how memory flows from time /inconstant, undependable,
/neither line nor circle // the soft wash of beauty” (P3);
“The children united /wanted to go upriver. / Only one
could swim, / but I would not say no. “ (DA, P5); “You,
here below and within, / are embraced by it all and called /
to your part in the dance. / Your heart opens and its drum-
sounds / are rhythms of life and gratitude.” (P6); “breathe
in / breathe out / wait wait / now? no / now? yes / go /
flow” (P10); “more dolphin / More waveform / A body
memory / wakes from a blue sleek time.” (P12); “Like
Pulse of life
Affirmation
Momentum
Love
FIVE FRACTAL GEOMETRIES FOR CREATIVE, SUSTAINABLE, JUST EDUCATION
21
Ecofractal
Pattern
With examples
Themes
from
Research
In Vivo Research Participant Sampler
Poem Excerpts (Detailed Credits in Appendix 1)
Liberation
Motifs
river water /that curves invisibly over a black stone, /
their dance answers our questions, / grants our wishes,
pulls us / out of the sea, the tomb, the snow” (P4)
Packing
Bee hive,
library, stellar
cluster
Proximity,
relationship,
closeness,
similarity,
togetherness,
storage
“Slow, undersea living / days lined like shapes on the skin
/ that fingers trace intimating / meaning: conjoin
conflux comrade / cooperate colloid collagen
colleague /kiss.” (DA, P5); “cocoon enclosure / rind
protected/ … hard bound knowledge /… packed in tightly”
(P10); “slow as a turtle, / ancient, wise, light as a cloud
swarm of peace” (P12); “life’s mouth / opens like a heart
cloud / in a living well of / layers / it could be /there are
millions /of planets /with life / and we have a choice / to
get sticky / and fertile with / not answers but /actual
pomegranate” (JF, P11)
Closeness, safety
Collaboration
Sharing
Resonance
Solidarity
Vortex
Spiral galaxy,
hurricane,
fingerprint
whorl
Change,
transformation,
memory
“brown speckled tunnel: /i hear the ocean now
/ curling in / elegant tapering / into the sound of justice /
justice – not just a word /a world, smiling” (P12);
“…where I sparkle in the / bitter still center, / then
ascend/descend / to remembering whorl/ of whole inner
outer self // perfect flat righteous love / of one spiraling
human / up, down, around again / remember forget remind
/ sustain// starts ringing rung out / fading and never / gone.
// starts ringing, facing, / and never silent /never gone,
never /spun out” (DA, P5); “spiny edges protruding /
watch out world / I’m being / expressing blessing /
witnessing” (P10); “you are more / than you know / that’s
why imagination / is” (JF, P11); “power lifts up / the one
thing / to the sky and puts / it down again // keep with this /
and you’ll / overcome something” (JF, P11); “echo in the
bones / of my ears to my spiral mind” (IS, P8)
Dynamic change
R/evolution
Integrity
(Actualization)
Justice
Rapidly opening
into something
larger that persists
Tapestry
(Pattern of
Patterns)
Basket weave,
spider web
weave,
coevolutionary
intertwining of
species in
biocultural
matrix
Harmony, scale
jumping,
embedment,
drawing
strength,
understanding
“j notices the tapestry but i see it / everywhere…/and span
outward to the packing of galaxies. / infrared maps of the
braille of space/ are structured in complex alphabets.
perhaps all our / answers are in the bumps of twigs” (P12);
“there are mysteries /right here on this /Earth that you
could / lay down upon / to look at the stars / your
sweetness known /to one of them, /who is not good at
/keeping secrets.//you are not just / a worker of what / must
be done / something in you / creates the sun / shine.” (JF,
P11) “What are the seeds / of the universe?//what are the
seeds of books? how can i save the / words of the world”
(P12); “rise up looking up to galaxies / looking down, see
the blue the / green dark & light day and /night woven //if
you reach with care considering all / sentient beings” (IS,
P8)
Coherence
Connectedness
Drawing strength
from
interdependence
and relatedness
Fluid /nimble
transpositionality
across complex
relationships
Note that the researcher is in the process of exploring alternate visualizations for these findings.
The researcher is aware of the irony of ecofractal findings being represented in a grid.
FIVE FRACTAL GEOMETRIES FOR CREATIVE, SUSTAINABLE, JUST EDUCATION
22
For simplicity in this reporting, convergent and divergent dimensions of ecofractals and their
liberatory motifs have been collapsed. Further doctoral scholarship is elaborating this in more
detail.
More detailed participant credits appear in Appendix 2 at the end of this paper.
Regenerativity of Group Work
To reprise, each of the sessions had one or more activities. Each activity produced one or
more work products which I scored using the incipient Transdisciplinary Regenerativity Index
(all references in this document refer to Transdisciplinary Regenerativity Index, version 1). A
scoring rubric of 0 (not present), 1 (present), 2 (exemplary or very present) were applied to each
of 51 possible regenerativity factors that could have been present. Each work product received
two evaluation numbers, one for the number of factors present (out of 51) and another for the
total scores across all factors (total could be up to 102).
The activities fall into two broad types: (1) those involving biomimicry or ecofractal
prompts (e.g., “the vortex” or ecofractal pattern cards), and (2) those using more general
complexity prompts (e.g., “symbiosis and collaboration”). Initial transdisciplinary regenerativity
index scoring demonstrates that all designs and group work products evidenced more than half of
the regenerativity factors (32 of 51, or greater, see Tables 1 and 3).
There was not significant difference between the more general and more specific
ecofractal prompt types on overall regenerativity scores. Using a Welch two-sided t-test, neither
the Regenerativity Scores (p = 0.740) nor the number of factors present (p = 0.837) were
significantly different between those activities using specific biomimicry and ecofractal prompts
and those sparked by the more general prompts.
That said, a finding worth exploring is that it seems as if different types of activities
might have been more effective at encouraging certain kinds of regenerativity in thinking and
design. For example, some of the biomimicry and ecofractal pattern-based work might not
FIVE FRACTAL GEOMETRIES FOR CREATIVE, SUSTAINABLE, JUST EDUCATION
23
emphasize cyclic processes; scores were lower for that type of regenerativity on biomimicry and
ecofractal group work products (i.e. inputs, outputs, exchanges; cycles). Some of the more
generic activities regarding complex adaptive systems were more effective for encouraging
design for feedback loops, but might need augmentation to influence participant regenerativity
factors such as cross-scale linkages and edges and margins. Few designs of either kind cultivated
natural phenomena self-sustaining the regenerative processes, so that indicates an area for further
cultivation of prompting.
The most significant finding from Group 1 research and Transdisciplinary Regenerativity
Index scoring at the group level was the cumulative score increases from repeated encounters
with the ecofractals. Fitting a linear model to the regenerativity scores (Group 1, across Sessions
1 and 2) versus the number of activities [using a regression of an ordinary least squares model
(OLS)], found a slope of +6.6 ±0.9 points per activity. In other words, over seven activities, over
the more than twelve months of the study, the Group 1 team experienced a significant cumulative
increase of six and half regenerativity points per activity that built upon the gains of the previous
activities. The p value of this coefficient is p = .000592. This means that it is 99.94% likely that
this training effect is not 0. The effect is very long-lasting, as these experiments took place across
a period of more than twelve months.
Potential limitations and caveats include that the events were not evenly spaced (seven
activities across two encounters, twelve months apart). It is unclear if the results are
generalizable, due to small sample size, small number of experiments, and high level of
education of Group 1 participants. Also, the scoring using the Transdisicplinary Regenerativity
Index is an interpretive activity. Finally, the usual caveats of ordinary least squares (OLS)
FIVE FRACTAL GEOMETRIES FOR CREATIVE, SUSTAINABLE, JUST EDUCATION
24
models apply. Nevertheless, the activity upon activity gain in regenerativity scores is significant
and merits further study.
The final IRB team design to catalyze online, self-organizing research communities via a
“research nest” design benefited from their earlier brainstorms and processes, so there are
potential successive learning effects present and more study is needed. To note, complexity
research does not seek to reductionistically isolate variables, so these types of synergistic effects
are actually desirable and demonstrate the emergent properties present in living systems research
and can reflect effective collaborative emergence. See Table 1 for workshop details and Table 3
for highlights of scores. These results are preliminary. This is the first time the Transdisciplinary
Regenerativity Index was used as a scoring tool and there is work currently underway on a fuller
version of the index that includes additional factors and sources.
Table 3
Group Creative Collaborations Raw Scores for Regenerativity in Design – Number of Total
Points and Number of Factors Present – Cumulative Learning Effect
(Using the Transdisciplinary Regenerativity Index, Version 1)
Brainstorm 1-
Biomimicry
Brainstorm 2 –
Complex Systems
Brainstorm 3 –
Systems & Stories
Brainstorm 4 -
Symbiosis &
Collaboration
20 Ethical Questions
for Researchers
(Revised)
Website Redesign –
Content Plan
"The Nest" Researcher
Community
Collaboration Support
"Po" Ecofractal
Brainstorm
Ecofractal Card
Group Poemstorm
Research Context
IRB,
Year 1
IRB,
Year 1
IRB,
Year 1
IRB,
Year 1
IRB,
Year 2
IRB,
Year 2
IRB,
Year 2
Tapestry,
Day 1
Tapestry,
Day 2
Prompt Type
Biomi
micry
Gener
al
Gener
al
Gener
al
Gener
al
Gener
al
Ecofr
actal
Ecofrac
tal
Ecofrac
tal
Total Raw Regenerativity
Score (out of 102 points)
49
50
68
74
72
81
89
86
67
% out of 102 Points
48%
49%
67%
73%
71%
79%
87%
84%
66%
Raw Number of Factors
Present (out of 51 factors)
36
32
41
46
46
48
49
48
41
% of 51 Factors Present
71%
63%
80%
90%
90%
94%
96%
94%
80%
Activity Number for
Regression
1
2
3
4
5
6
7
NA
NA
FIVE FRACTAL GEOMETRIES FOR CREATIVE, SUSTAINABLE, JUST EDUCATION
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For the total score of activities 1-7, there is an increase for the long-term team of +6.6 ±0.9
points for each activity. T statistic is 7.691. Given the degrees of freedom and the T statistic, the
p = .000592. This means it is 99.94% likely that these results are not zero. Tested via linear
regression, looking for a training effect using R 3.0.0 software.
Individual Effects of the Research
As a portion of the pre- and post-experience testing (administered starting with Group 1,
Session 2), ecofractal participants assessed how Creative, Hopeful, Inspired, and Connected to
the earth and others they felt before and after each session using the CHIC instrument.
Comparing the pre- and post- testing, for both groups, participants reported significant increases
in feeling creative, hopeful, inspired, and connected to the Earth and others. Results reflect using
a Wilcoxon signed rank test with continuity correction for small group sizes using a 10% level of
significance on R software. For both Group 1 and Group 2, participants self-scoring increased
significantly along all four dimensions: feeling creative, hopeful, inspired, and connected to
Earth and others. See Table 4 for details.
Table 4
Summary Findings, Pre and Post Test Results and Significance for Participants Feeling
Creative, Hopeful, Inspired, and Connected to the Earth and Others (CHIC self-evaluation
instrument) for Group 1, Session 2 and Group 2 (Wilcoxon signed rank test)
Quality of the CHIC Instrument - Participants and
Facilitators
Groups
Creative
Hopeful
Inspired
Connected to
Earth &
Others
Research Ethics
Team (Session 2)
(Session 2 Pre-test &
Post-test)
0.0868*
0.0868*
0.0473**
0.0445**
The Great Tapestry
Workshop
(Day 1 Pre-test & Day
2 Post-test)
0.00354***
0.0200**
0.00961***
0.0168**
FIVE FRACTAL GEOMETRIES FOR CREATIVE, SUSTAINABLE, JUST EDUCATION
26
Calculations using a 10% level of significance, participant self-assessment pre and post-
experience, calculating using R 3.0.0 software - Wilcoxon signed rank test with continuity
correction for small group sizes. This is a one-sided test.
* p < .10, ** p < .05, *** p <.01
Discussion & Significance
Educators and ecopsychologists notice the diminishing nature languages of human-nature
interaction (Kahn, Ruckert, Severson, Reichert & Fowler, 2010) and the subsequent losses to
students, cultures, systems, and psyche. Earth system decoherence as a result of industrial
extraction and pollution threaten peoples and ecosystemic integrities. And the contracting
constructs around sustainability will determine if the latest efforts at reclamation are coopted as a
new form of development or liberated into more holistic, ancient, regenerative patterns of
congruence and restoration. In a world of increasing industrial grid, fractal geometries hold
promise as liberating alternatives to reconnect learners with incipient, alive patterns from the
living earth and biocultural matrix.
Ecofractals can catalyze perceptual openness and complexity. They can help creative
groups achieve collaborative emergence (a la Sawyer, 2010) to awaken novel, sustainability-
informed, and just solutions to educational and cultural challenges. The findings regarding
significant and sustained successive increases in regenerativity as a result of creative
collaboration with ecofractals, as well as the findings of significant increases in feeling creative,
hopeful, inspired, and connected to earth and others indicate polyscale personal and collective
promise in ecofractal creative collaborations. In particular, the findings of successive increases in
regenerativity suggest a possible auto-catalytic, autopoietic effect of creating together sparked by
ecofractals. This confirms the possibilities of nature- and bioculture- informed creative
collaboration catalyzing a kind of personal and group regenerative creativity.
FIVE FRACTAL GEOMETRIES FOR CREATIVE, SUSTAINABLE, JUST EDUCATION
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Perhaps beyond the new-product innovations of biomimicry (Biomimicry 3.8 Institute,
2013), ecofractals can catalyze systems-level “ecomimicry” to increase the collaborative synergy
of peoples, cultures, and planetary contexts to nourish and support learners and systems
strengthened to evolve to produce (and/or affirm existing) locality-relevant patterns of learning
and thriving.
These findings are resonant with ecojustice and indigenous education insights. For
example these ecofractal-inspired findings harmonize with Kawagley and Barnhardt’s
description of indigenous contributions to ecological and educational understanding (1999, p.
134), including long-term perspective (system memory), interconnectedness of all things (an
emergent finding in the research), adaptation to change (as evidenced in the vortex pattern), and
commitment to the commons (expressed via the hive/packing pattern). They are consonant with
Cajete’s orientations in the development of indigenous science education (2008), including
being holistic, integrated, interdisciplinary, experiential, twinned with the “use of metaphoric
communication” and experience in nature and bioculture, “honoring the essential importance of
direct experience, interconnectedness, relationship, holism, quality, and virtue” (pp. 489-491). It
connects with diversity, democracy, and sustainability which are core community values in
ecojustice education (Martusewicz, Edmundson & Lupinacci, 2011).
This research promises to address a challenge in sustainability education, how to
integrate the seemingly competing demands of an education that increases regenerativity and
resilience for individual learners’ experience and one that optimizes for educational and societal
sustainability outcomes (Sterling, 2010). The findings indicate that there is a prosperity in fractal
geometries when applied to group creativity. Both longitudinal and point in time interventions
using ecofractals demonstrated individual and group benefits in alignment with biocultural and
FIVE FRACTAL GEOMETRIES FOR CREATIVE, SUSTAINABLE, JUST EDUCATION
28
planetary health. From living systems research contexts actively increasing education and
consciousness raising about cultural and anthropocentric bias and exclusionary research design,
to ecologically-inspired college support structures, to poetically-inspired cultural resurgence, this
ecofractal group research demonstrated productive possibilities in sustainability and social
justice. The outcomes were regenerative and the creative processes also personally restorative.
Both in process and outcome, the groups discussed demonstrate how diversity and creativity
require openness and can yield justice.
To note, several issues arise for further study. It is possible emergent effects of
participant embodiment and detailed physical experience with prompts may have had an
unanticipated influence on outcomes. For example, in “The Great Tapestry” workshop (Group
2), the participants ended up cradling and holding the branch prompt items in their own arms due
to the size of the materials. This might have effectively been mirrored or reflected in the
“reaching out” theme that emerged from the ecofractal pattern of branching. Is it possible that the
packing prompts being passed in a circle or the fact that the participants relied on visual
representation as catalysts affected the amount that the packing prompt evoked metacognition
and “thinking about” rather than immersion [though this finding was not universal; some
participants in packing were still evidencing empathic placing of themselves into the prompt
subject(s)]? Future research could extend the scope of research to extend a dimension of
ecofractal physicality, perhaps exploring different physical approaches within one ecofractal
and/or explore tailoring the means of ecofractal prompt resonant with each pattern. This could be
resonant with the work of Barbara Widhalm (2011) who extended Capra’s six living systems
patterns (2004) to somatic and emotional interpretations, as well as along the lines of dance
researcher Andrea Olsen’s Body and Earth: An Experiential Guide (2002) and/or Ann Amberg’s
FIVE FRACTAL GEOMETRIES FOR CREATIVE, SUSTAINABLE, JUST EDUCATION
29
(2011) spatial, mandalic, and principled interpretation of Brian Swimme’s “The Powers of the
Universe” (2004). Other areas of my research, including the Vortex single ecofractal focus
workshop, did explore more of this embodied resonance prompt experimentation, and those
results though outside of the current survey will be exciting to unfold in future scholarship.
Nature immersion is more than pain relief; it offers regeneration of emplacement within
the enclosing, nested congruities, what Freya Mathews terms “conative gestalts” (2008).
Participants reported feelings of significantly increased creativity and hopefulness, inspiration
and connectedness.
Research has clearly demonstrated that dissent and diversity is crucial to effective group
collaboration (Milliken, Bartel & Kurtzberg, 2003; Nemeth & Nemeth-Brown, 2003). Yet
perturbation and dissent can be uncomfortable. Is it possible that marveling together at, and
inhabiting, natural and biocultural majesties of resonant fractal geometries that span multiple
scales of perception can help ease these discomforts? Can processes of mutual submerging in
larger unities as well as the honoring of difference inherent in ecofractal approaches help
support, contain, and nurture our mutual catalytic growth? Perhaps the emerging liberatory
motifs can provide help: of reaching out, clarity, and self-determination (branching); inclusion
and belonging (radiance), affirmation and momentum (flow), collaboration and sharing
(packing), and dynamic change and integrity (vortex).
Further, the harmonic emergence of drawing strength from interdependence and
relatedness as well as fluid /nimble transpositionality across complex relationships arising from
the multiplicity of pattern and scale (within tapestry/ weave) can gird us for our journey beyond
the grid, and open the way ahead. This research demonstrates the fruits of what Davis and
Sumara describe as the ability to “level jump” across scales, and how it allows us to
FIVE FRACTAL GEOMETRIES FOR CREATIVE, SUSTAINABLE, JUST EDUCATION
30
“simultaneously examine a phenomenon in its own right… and pay attention to the conditions of
its emergence” (2008, p. 34). This kind of systems-level metacognition can help students and
system instigators learn to collaborate to emerge beyond system constraints into novel
(ancient/renewed/new) synergies of classroom and educational systems. These gyres of
emergence can be a route to educational emergence and regeneration (Hauk, 2011). Creating
enduring changes in educational systems inspired by living systems approaches (Mitchell &
Sackney, 2009) invite us to be a part of this regenerative emergence.
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Appendices
Appendix 1
Research Participant Credits
(Identified Reflective of Participant Preference)
Prescott College Institutional Review Board Design Team (2011-2012)
CS Camille Smith – Graduate Faculty, Counseling Psychology, Director - Expressive
Arts Therapy Institute
DH Doug Hulmes, Professor of Environmental Studies and Education
MH Marna Hauk (researcher-participant) – Doctoral Student, Sustainability Education;
Master of Arts Faculty
MWH Michaela Willi Hooper – Graduate Reference Librarian
NCC Noël Cox Caniglia – Graduate Chair of Education
NEF Nina Ekholm Fry – Director, Equine Assisted Mental Health, Associate Faculty,
Counseling Psychology
The Great Tapestry Workshop (September 2012)
P2 (CN P2) Claire Nail
P3 (P3) Name anonymized at participant request
P4 (P4) Name anonymized at participant request
P5 (DA P5) Daniel Ari
P6 (P6) Name anonymized at participant request
P8 (IS P8) Ila Suzanne Grey
P9 (BD P9) Birch Dwyer
P10 (P10) Name anonymized at participant request
P11 (JF P11) John Fox (co-facilitator, participant)
P12 (P12) Name anonymized at participant request
Note, Tapestry participants 1 and 7 were preregistered but dropped out before the start of the
workshop and participants 9 and 10 substituted in by start time, to maintain participant numbers.
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39
Appendix 2
Poetic Prompts
Workshop Theme Poem
Sonnets to Orpheus, Part 2, Poem XXI – Rainier Maria Rilke (Translated by Anita
Barrows & Joanna Macy)
Branching
Woods - Wendell Berry
* Excerpt, Manifesto: Mad Farmer Liberation Front – Wendell Berry
Radiance
The First Roots Creep Up – Deena Metzger
Web – Denise Levertov
Earth as Sentient Being – David Abram (Excerpt from Becoming Animal)
Light Years – Joan Swift
Flow
River, O River – Julia Older
On Creativity – Martha Graham
Ask Me – William Stafford
Packing
The Woman I Love is a Planet; The Planet I Love is a Tree (Excerpt) – Paula Gunn Allen
A Bowl - Rumi
Kneeling Here, I Feel Good – Marge Piercy
Contradictions: Tracking Poems, Part 18 – Adrienne Rich
Vortex
Gyre – Aimée deChambeau (was read out loud)
Harmony (Patterns of Patterns)
Sands of the Well (Excerpt) – Denise Levertov
Bonus: Meditation from Joanna Macy & John Seed
ResearchGate has not been able to resolve any citations for this publication.
Book
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Years ago, while a secondary-level student teacher (I was getting a teaching credential in physics and math, and also in visual arts), a friend asked me if I would visit the fourth- through six-grade class at a small and quite charming three-room schoolhouse – truly a little wooden house – in a quaint rural California town, to teach a guest science lesson. I was learning some good things and wanted to try them out, so I said, “Sure!” There were three schoolrooms: My friend's personally designed classroom (K–3), the upper elementary room (4–6), and finally what was at that time called a junior high school (7–8) – here the junior high school room. My friend's K-3 room had the distinction of red and white-checkered curtains, special areas, and clustered furniture, a very homey feel, and she often played music, especially classical, for the kids. As I recall, there was a lot of time for reading and thinking, and I can picture them happily scattered on the floor with their books, on large cushions. They also got to ask lots of questions. I was encouraged – surely my own creative lesson plan would be welcome. I was training to work with secondary-level kids, not with fourth- through six-graders. But I was bringing challenging activities for any age, I thought; surely my attempts would be appreciated. Yet, as it turned out, they were not appreciated by everyone. This experience has actually motivated me for years.