Evolutionary Automaton - The Bak-Sneppen Model

[kram1032]

I made this image according to the rules of the Bak-Sneppen Model EDIT: Code updated to have an actually working mutation process. It previously did nothing. A super-simple model of co-evolution. You can find a more indepth explanation as well as a javascript simulation here Furthermore, here is my Mathematica Implementation, that produced the image you can see on the left. It should be pretty straightforward to port to other languages. Code: (* User Parameters *) len = 100; (* Population-size = list-length *) count = 1000; (* While loop counter - number of timesteps *) mRate = .001; (* Mutation rate *) (*Initialization*) data = RandomVariate[UniformDistribution[],   len]; (* generate a list of random variables *) mat = {data}; (* put generated data into a second list level - this \ will be the output matrix *) (*Main Program*) While[count > 1,  smallest =   Ordering[data][[1]];(* find the element with the smallest value *)  replace =   RandomVariate[UniformDistribution[],    3];(* build a list of replace values *)  data = If[1 < smallest < len,    ReplacePart[     data, {smallest - 1 -> replace[[1]], smallest -> replace[[2]],      smallest + 1 -> replace[[3]]}], (*    replace the correct array positions *)    If[smallest == 1,     ReplacePart[      data, {len -> replace[[1]], 1 -> replace[[2]],       2 -> replace[[3]]}], (* special-cases for borders *)     ReplacePart[      data, {len - 1 -> replace[[1]], len -> replace[[2]],       1 -> replace[[3]]}]]]; (*in order to make it a full circle *)    mat = Append[mat, data]; (* add a line to the history *)  (* initialize Mutation *)  i = 1;  mArray =   RandomVariate[UniformDistribution[],    len]; (*generate a List of random variables. Again. *)    While[i < len,       If[mArray[[i]] < mRate,      data = ReplacePart[data,         i -> RandomVariate[UniformDistribution[]]];] (*     if the variables are below the mutation rate,     replace the data with a random value *)     i++]         count--] (*make sure, the two while loops finish *) MatrixPlot[mat, ColorFunction -> "TemperatureMap", Frame -> False,  PixelConstrained -> 1](*plot with pretty colors*) Enjoy! The Bak-Sneppen Model is an example of Self-organized criticality Here is the corresponding Wiki. It also includes a neat image to show how complex these can be: I believe, this graph is time-colored. - Mine is based on fitness.