three famous plots of chaos

#Plots Feigenbaum diagram: divides the parameter interval [2,4] for mu #into N steps. For each value of the parameter, iterate the discrete #dynamical system x->mu*x*(1-x), drop the first M1 points in the orbit #and plot the rest in (mu,x) diagram N=200 M1=200 M2=200 x0=0.509434 puntos=[] for t in range(N): mu=2.0+2.0*t/N x=x0 for i in range(M1): x=mu*x*(1-x) for i in range(M2): x=mu*x*(1-x) puntos.append((mu,x)) point(puntos,pointsize=1) 

#Lorentz attractor #plots the orbit of the point (1,1,1) using the simplest euler method h=0.01; # time step k=2000 # number of iterations (time k*h will be reached) sigma=10; #parameters rho=28; beta=8/3; x=1; y=1; z=1; # initial data puntos=[] for i in range(k): x,y,z=x+h*( sigma*(y-x) ), y+h*( x*(rho - z) - y ), z+h*( x*y - beta*z ) puntos.append((x,y,z)) point3d(puntos) 

#Mandelbrot set: the final plot is a subset of the complex plane; #the color at point c is porportional to the number of iterations that #the discrete dynamical system z->z^2+c takes to leave a circle around #the origin when z0=0 N=100 #resolution of the plot L=50 #limits the number of iterations x0=-2; x1=1; y0=-1.5; y1=1.5 #boundary of the region plotted R=3 #stop after leaving the circle of radius R m=matrix(N,N) for i in range(N): for k in range(N): c=complex(x0+i*(x1-x0)/N, y0+k*(y1-y0)/N) z=0 h=0 while (h<L) and (abs(z)<R): z=z*z+c h+=1 m[i,k]=h matrix_plot(m)