International Society of Quantum Biophysical Semeiotics, Treviso, Italy
Question
Asked 15th Jul, 2014
Are snowflakes based on fractal geometry?
A snowflake is either a single ice crystal or an aggregation of ice crystals which falls through the Earth's atmosphere. They begin as snow crystals which develop when microscopic supercooled cloud droplets freeze. Snowflakes come in a variety of sizes and shapes. Complex shapes emerge as the flake moves through differing temperature and humidity regimes, such that individual snowflakes are nearly unique in structure. Snowflakes encapsulated in rime form balls known as graupel. Snowflakes appear white in color despite being made of clear ice. This is due to diffuse reflection of the whole spectrum of light by the small crystal facets. (Wikipedia)
Most recent answer
"Indeed, at the end of the day the real reason about fractals in snowflakes is to be discovered."
Fractals is strictly connected with deterministic chaos, entropy and information, therefore it would be interesting to face the topic with all these details. For example, if we have a look on Emoto crystals, we can perceive self-similarity properties in the crystals, we can think of fractals too, and we know that those crystals come from informed water. Information means "to give form", to in-form, as suggested by David Bohm too. A snowflake can be viewed also as all the set of information that give it form during the path. In nature all snowflakes are different each other, each snowflake is unique. This is why snowflake is a typical example of an element in nature with SDIC (sensitive dependence on initial conditions), i.e., with deterministic chaos.
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Popular answers (1)
El Bosque University
This question allows for two quite different answers, and yet equally valid - provided that one either takes one or the other; not both at the same time.
First, snowflakes are indeed based on fractal geometry - if one takes fractal geometry in an ontological sense. Various authors can be cited to support this line.
Yet, on the other side, one can safely say that, on the contrary, it is thanks to fractal geometry that we can explain the structure of figures such as a snowflake. Again, a number of texts ban be cited here as support.
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All Answers (7)
El Bosque University
This question allows for two quite different answers, and yet equally valid - provided that one either takes one or the other; not both at the same time.
First, snowflakes are indeed based on fractal geometry - if one takes fractal geometry in an ontological sense. Various authors can be cited to support this line.
Yet, on the other side, one can safely say that, on the contrary, it is thanks to fractal geometry that we can explain the structure of figures such as a snowflake. Again, a number of texts ban be cited here as support.
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University of Western Australia
google scholar fractal snowflake
The first hit is Mandelbrot's book, the second in a 1983 paper by Stanley's group:
'nuff said.
Georgia Institute of Technology
I intend this answer as an elaboration on Carlos's answer.
Based on? In one sense, no. When a snowflake forms, it is rotating while falling through high-humidity cold air. The snowflake grows at its perimeter. The heat released from the phase change creates little plumes or vortices that are thought to be what makes it rotate. This isn't a fractal-creating process per se, as compared with the turtle geometry algorithms used to mimic seashells, or the recursive use of a linear function to generate a fractal. Snowflakes don't have perfect symmetry.
However, it is a remarkable fact that fractals can very closely approximate real snowflakes. When a simple mathematical model accurately captures 95% or 99% of the structure of a natural phenomenon, there usually is a deep insight about the physical process to be gained. In that sense, yes.
The last time I studied this phenomenon, it was still not understood why many snowflakes have 6-fold symmetry. (Not all of them do). Hydrogen bonds explain that on the molecular level, of course, but they don't explain it at all on the macro level. As an analogy, a shape cut out from a square mesh need not be a square. As a closer analogy, if you put a bunch of square tiles together, you don't necessarily get a square shape. So as best I know, the deep insight explaining why fractals so closely approximate snowflakes has not been discovered.
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El Bosque University
Fantastic, dear Craig. Thank you so much. A very helpful elaboration. Indeed, at the end of the day the real reason about fractals in snowflakes is to be discovered. As yet, fractal geometry is a far better approximation to understanding such phenomena - as it has been largely shown in the literature.
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International Society of Quantum Biophysical Semeiotics, Treviso, Italy
"Indeed, at the end of the day the real reason about fractals in snowflakes is to be discovered."
Fractals is strictly connected with deterministic chaos, entropy and information, therefore it would be interesting to face the topic with all these details. For example, if we have a look on Emoto crystals, we can perceive self-similarity properties in the crystals, we can think of fractals too, and we know that those crystals come from informed water. Information means "to give form", to in-form, as suggested by David Bohm too. A snowflake can be viewed also as all the set of information that give it form during the path. In nature all snowflakes are different each other, each snowflake is unique. This is why snowflake is a typical example of an element in nature with SDIC (sensitive dependence on initial conditions), i.e., with deterministic chaos.
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