View source for Evolutionary Kaleidoscopes in the Prisoner's Dilemma

For deterministic update rules (synchronous lattice update, best player in neighborhood reproduces) and symmetrical initial configurations this can lead to fascinating spatio-temporal patterns. Such evolutionary kaleidoscopes are certainly only of limited scientific interest but they do have quite some entertainment value.
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Image:Kaleidoscope Prisoner's Dilemma (t=0).png|<math>t=0</math>

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Image:Kaleidoscope Prisoner's Dilemma (t=100).png|<math>t=100</math>

Image:Kaleidoscope Prisoner's Dilemma (t=150).png|<math>t=150</math>

Image:Kaleidoscope Prisoner's Dilemma (t=200).png|<math>t=200</math>

Image:Kaleidoscope Prisoner's Dilemma (t=250).png|<math>t=250</math>

Image:Kaleidoscope Prisoner's Dilemma (t=300).png|<math>t=300</math>

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Image:Kaleidoscope Prisoner's Dilemma (t=500).png|<math>t=500</math>

Image:Kaleidoscope Prisoner's Dilemma (t=550).png|<math>t=550</math>

Image:Kaleidoscope Prisoner's Dilemma (t=600).png|<math>t=600</math>

Image:Kaleidoscope Prisoner's Dilemma (t=650).png|<math>t=650</math>

Image:Kaleidoscope Prisoner's Dilemma (t=700).png|<math>t=700</math>

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==EvoLudoLab==

{{EvoLudoLab:2x2|
options="--delay 200 --view 0 --reportfreq 1.0 --popsize 101x --popupdate s --playerupdate b --updateprob 1.0 --switchpref 0.0 --geometry n --intertype a1 --numinter 1 --reprotype a4 --initfreqs 0:1 --mutation 0.0 --basefit 1.0 --selection 1.0 --reward 1.0 --punishment 0.0 --temptation 1.4 --sucker 0.0"|
title=Spatial Prisoner's Dilemma: evolutionary kaleidoscopes|
doc=For symmetrical initial configurations and determinsitic update rules fascinating spatio-temporal patterns resembling evolutionary kaleidoscopes can emerge in spatially structured populations where individuals are arranged on a lattice and interact only within a limited local neighborhood. Different values for the paramters <math>R, S, T</math> and <math>P</math> give rise to different types of kaleidoscopes. Here we set <math>R = 1, P = 0, S = 0.0</math> and<math>T = 1.4</math> and individuals interact with their four nearest neighbors on a square <math>101\times 101</math> lattice with periodic boundary conditions.

Patient people will find that the evolving patterns come to a sudden an unexpected end after more than 200'000 generations (MC steps) when the system relaxes into a cyclic state with short period. The time until an absorbing or cyclic state with short period is reached sensitively depends on the lattice size. Interestingly there is no simple relation between system size and relaxation time.}}

[[Category: Christoph Hauert]]