Python program simulating cellular automaton r-GoL that represents robust generalization of 'Game of Life'
Abstract
<<< The code is a part of the paper: https://www.researchgate.net/publication/361818826_Robust_massive_parallel_information_processing_environments_in_biology_and_medicine_case_study >>>
The presented emergent structures were discovered during research on modifications of the 'Game of Life' proposed by John Conway, which are aiming towards discovery of robust emergents, that are immune to randomly injected faulty evaluations. See details in the paper, the link is provided below, where those simulations are presented only in figures.
Many scientifically and visually appealing simulation had arisen there, where the observed structures might be interesting to researchers working in biology and other disciplines. Animations are always having a great expressive power, see PNG animations below. Make sure that the viewer can display animated PNG figures!
In general, it is observed that emergent structures of various types arise within this specific cellular automaton, all of them are having the period of two. What is surprising is the fact that those structures are long-range correlated, and some of them even turn by ninety degrees.
From a certain point of view, we can say that the observed emergents posses a very stable binary behavior that deserves a deeper study. Surprisingly, no moving emergents were observed in this type of cellular automaton.
...... .......
Simulated videos of the code runs are shown at the link:
https://www.researchgate.net/publication/357285926_Python_program_simulating_cellular_automaton_r-GoL_that_represents_robust_generalization_of_%27Game_of_Life%27_sample_runs
...... .......
The software belongs to the paper that is available here:
https://www.researchgate.net/publication/361818826_Robust_massive_parallel_information_processing_environments_in_biology_and_medicine_case_study/
File (1)
Content uploaded by Jiří Kroc
Author content
... When those generalizations are implemented into the GoL, an improved, more robust algorithm is defined that is called the r-GoL, see Algorithm 1 [27]. ...
... Both methods had been tested and evaluated as documented in this section. Robustness of emergent structures observed within r-GoL is clearly demonstrated, see the open-source codes and animations of both algorithms in [20,27]. ...
... PCG64(124)) as it progresses into a set of stable corralled domains of alternating patterns: points and arrows. Snapshots are taken at the times: 0, 35, 36, 100, 101, and 185, see [27]. 4. Snapshots of the diffusion patterns evolution are shown for the identical initial conditions and times as in Fig. 3. Displayed sub-figures correspond one-to-one in both figures, see [27]. ...
The current frontiers in the description and simulation of advanced physical and biological phenomena observed within all scientific disciplines are pointing toward the importance of the development of robust mathematical descriptions that are error resilient. Complexity research is lacking deeper knowledge of the design methodology of processes that are capable to recreate the robustness, which is going to be studied on massive-parallel computations (MPCs) implemented by cellular automata (CA). A simple, two-state cellular automaton having an extremely simple updating rule, which was created by John H. Conway called the ’Game of Life’ (GoL) is applied to simulate and logic gate using emergents. This is followed by simulations of a robust, generalized GoL, which works with nine states instead of two, that is called R-GoL (open-source). extra states enable higher intercellular communication. The logic gate is simulated by the GoL. It is destroyed by injection of random faulty evaluations with even the smallest probability. The simulations of the R-GoL are initiated with random values. several types of emergent structures, which are robust to injection of random errors, are observed for different setups of the R-GoL rule. The GoL is not robust. The R-GoL is capable to create and maintain oscillating, emergent structures that are robust under constant injection of random, faulty evaluations with up to 1% of errors. The R-GoL express long-range synchronization, which is together with robustness facilitated by designed intercellular communication. ..... ...... ..... ..... (Software & video links available at the file Software-and-animation-links-to--r-GoL.txt, see below)
... A randomly chosen cell with the probability p = 0.0001 get reversed its value. The sequence of snapshots taken at steps 0,10,49,88,200, and 300 that are depicting a glider gun emitting gliders, gliders, copperhead ship, stable configuration, and blinker will get quickly disrupted and destroyed, see videos (Kroc, 2022). ...
... A threshold that represents silencing of an overexcited cell is defined as T D . When those generalizations are implemented into the GoL, an improved, more robust algorithm is defined that is called the r-GoL, see Algorithm 1 (Kroc, 2022). During simulation of the r-GoL from a random initial condition, various static and oscillating structures having the period of two (blinkers) emerges after some transition period. ...
>>> Read the improved, published version with links to the Python software and animations here: https://www.researchgate.net/publication/361818826_Robust_massive_parallel_information_processing_environments_in_biology_and_medicine_case_study <<< ...... The current frontiers in the description and simulation of advanced physical and biological phenomena observed within all scientific disciplines are pointing directly toward the importance of development of robust mathematical descriptions that are error resilient. Complexity research is lacking deeper knowledge of the design methodology of processes that are capable to recreate the robustness. The first, introductory part of the paper provides a concise introduction into this difficult research area to non-specialists. This is followed by the second part, which is focusing on a description, that is providing a certain level of the desired robustness. The first part is describing the basic principles of massive-parallel computations (MPC) that are demonstrated on a simple cellular automaton having an extremely simple updating rule, which was created by John H. Conway: the 'Game of Life' (aka the GoL). This allows us to enter the second, research part dealing with a simple CA rule, which is a generalization of the GoL, that is possessing an increased robustness against errors along with a very interesting set of emergent structures that are expressing longrange synchronization.
ResearchGate has not been able to resolve any references for this publication.