""" Langton's loop ============== Chris Langton created the "loop" cellular automata to illustrate how a cellular automata `can self-reproduce `_. Here is a video of Langton's loop. .. youtube:: Umf1QzONBx0 :width: 640 :height: 349 The code below is adapted from an implentation by Romain Fontaine (Copyright 2018) """ import numpy as np import matplotlib.pyplot as plt from pylab import rcParams def show_grid(ax,grid,make_animation): N=np.size(grid,1) if make_animation: frame = ax.imshow(grid, cmap=plt.get_cmap('Blues'), interpolation='nearest',animated=True) else: frame = ax.imshow(grid, cmap=plt.get_cmap('Blues'), interpolation='nearest') ax.spines['top'].set_visible(False) ax.spines['right'].set_visible(False) ax.spines['left'].set_visible(False) ax.spines['bottom'].set_visible(False) ax.set_ylim(0,N) ax.set_xlim(0,N) ax.set_xticks([]) ax.set_yticks([]) ax.axis('equal') return frame def iterate(grid,new_value): N=np.size(grid,1) new_grid = np.zeros((N, N), dtype="int") for i in range(N): for j in range(N): new_grid[i,j]=new_value(i, j,grid) return new_grid, grid ############################################################################## # Now we set up the cellular automata N = 120 STEPS = 800 def initialize(): init_pattern = ["02222222200000", "21701401420000", "20222222020000", "27200002120000", "21200002120000", "20200002120000", "27200002120000", "21222222122222", "20710710711111", "02222222222222"] for i, line in enumerate(init_pattern): for j, char in enumerate(line): grid[i+int(N/2)-5, j+int(N/2)-15] = int(char) ############################################################################## # And set up the rules and a function which applies them. rules = { # format: "CNESW":"C" "00000":"0","00001":"2","00002":"0","00003":"0","00005":"0","00006":"3","00007":"1","00011":"2","00012":"2","00013":"2","00021":"2", "00022":"0","00023":"0","00026":"2","00027":"2","00032":"0","00052":"5","00062":"2","00072":"2","00102":"2","00112":"0", "00202":"0","00203":"0","00205":"0","00212":"5","00222":"0","00232":"2","00522":"2","01232":"1","01242":"1","01252":"5", "01262":"1","01272":"1","01275":"1","01422":"1","01432":"1","01442":"1","01472":"1","01625":"1","01722":"1", "01725":"5","01752":"1","01762":"1","01772":"1","02527":"1","10001":"1","10006":"1","10007":"7","10011":"1","10012":"1", "10021":"1","10024":"4","10027":"7","10051":"1","10101":"1","10111":"1","10124":"4","10127":"7","10202":"6", "10212":"1","10221":"1","10224":"4","10226":"3","10227":"7","10232":"7","10242":"4","10262":"6","10264":"4", "10267":"7","10271":"0","10272":"7","10542":"7","11112":"1","11122":"1","11124":"4","11125":"1","11126":"1", "11127":"7","11152":"2","11212":"1","11222":"1","11224":"4","11225":"1","11227":"7","11232":"1","11242":"4", "11262":"1","11272":"7","11322":"1","12224":"4","12227":"7","12243":"4","12254":"7","12324":"4","12327":"7", "12425":"5","12426":"7","12527":"5","20001":"2","20002":"2","20004":"2","20007":"1","20012":"2","20015":"2", "20021":"2","20022":"2","20023":"2","20024":"2","20025":"0","20026":"2","20027":"2","20032":"6","20042":"3", "20051":"7","20052":"2","20057":"5","20072":"2","20102":"2","20112":"2","20122":"2","20142":"2","20172":"2", "20202":"2","20203":"2","20205":"2","20207":"3","20212":"2","20215":"2","20221":"2","20222":"2","20227":"2", "20232":"1","20242":"2","20245":"2","20252":"0","20255":"2","20262":"2","20272":"2","20312":"2","20321":"6", "20322":"6","20342":"2","20422":"2","20512":"2","20521":"2","20522":"2","20552":"1","20572":"5","20622":"2", "20672":"2","20712":"2","20722":"2","20742":"2","20772":"2","21122":"2","21126":"1", "21222":"2","21224":"2","21226":"2","21227":"2","21422":"2","21522":"2","21622":"2","21722":"2","22227":"2","22244":"2", "22246":"2","22276":"2","22277":"2","30001":"3","30002":"2","30004":"1","30007":"6","30012":"3","30042":"1", "30062":"2","30102":"1","30122":"0","30251":"1","40112":"0","40122":"0","40125":"0","40212":"0","40222":"1", "40232":"6","40252":"0","40322":"1","50002":"2","50021":"5","50022":"5","50023":"2","50027":"2","50052":"0", "50202":"2","50212":"2","50215":"2","50222":"0","50224":"4","50272":"2","51212":"2","51222":"0","51242":"2","51272":"2", "60001":"1","60002":"1","60212":"0","61212":"5","61213":"1","61222":"5","70007":"7", "70112":"0","70122":"0","70125":"0","70212":"0","70222":"1","70225":"1","70232":"1","70252":"5","70272":"0" } def new_value(i, j,grid): c = str(grid[i, j]) a = [str(grid[(i-1)%N, j]), str(grid[i, (j+1)%N]), str(grid[(i+1)%N, j]), str(grid[i, (j-1)%N])] for i in range(4): # Try every rotation of this array: [TOP, RIGHT, BOTTOM, LEFT] try: return rules["".join([c, a[i%4], a[(i+1)%4], a[(i+2)%4], a[(i+3)%4]])] except KeyError: pass return grid[i, j] # if no rule is found, return the previous value ############################################################################# # # Now we simulate the model printing out every 50th step # import matplotlib.pyplot as plt import matplotlib.cm as cm import matplotlib.animation as animation grid = np.zeros((N,N), dtype="int") rcParams['figure.figsize'] = 20/2.54, 20/2.54 initialize() fig,axs=plt.subplots(4,4) count=0 count2=0 for i in range(STEPS): grid, old_grid = iterate(grid,new_value) # Iterate & swap the two grids if (np.mod(i,50)==0): show_grid(axs[count][count2],old_grid,0) count=count+1 if count>=4: count2=count2+1 count=0 plt.show() ############################################################################# # # Make a video # make_animation=0 if make_animation: grid = np.zeros((N,N), dtype="int") initialize() img = [] # some array of images frames = [] # for storing the generated imagesfig, ax = plt.subplots() fig,ax=plt.subplots(1) for step in range(STEPS): grid, old_grid = iterate(grid,new_value) # Iterate & swap the two grids im = show_grid(ax,old_grid,1) frames.append([im]) ani = animation.ArtistAnimation(fig, frames, interval=50, blit=True, repeat_delay=1000) # set output file writer = animation.FFMpegWriter(fps=15, metadata=dict(artist='Me'), bitrate=1800) ani.save("Langtons_Loop_movie.mp4", writer=writer)