Thanks Pablo. Very useful. I posted this to the wiki: http://wiki.sagemath.org/pics Let me know if this is okay since everything posted to the wiki gets licensed under http://creativecommons.org/licenses/by-sa/3.0/ (So if you don't reply I will have to remove it.) - David Joyner
On Sat, Sep 13, 2008 at 6:23 AM, Pablo Angulo <[EMAIL PROTECTED]> wrote: > > Hello: > First I'd like to greet everyone and thank each person responsible for > this great improvement to mathematical software. Sage is a better > solution for the teaching of mathematics at university level than any > other software package for most tasks. > I'll be using the software for teaching next year and, as a > preparation, I'm trying to get used to the software. I've published a > worksheet called "three famous plots of chaos", with the feigenbaum, > lorentz and mandelbrot plots. It's available at: > > https://sage.math.washington.edu:8101/home/pub/3 > > I'd really appreciate any comment, and apologize in advance if I > overlooked similar previous work. Just one final comment: as you know, > quality plots of these diagrams take a lot of computer time, so I'd > suggest we don't all use the scarce servers, and use our own > installations of sage whenever possible for testing these plots. The > three snippets that generate the plots follow. > > Regards > Pablo Angulo > > ----------------------------------- > > #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 next M2 points in a (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) > > > > > > --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "sage-edu" group. To post to this group, send email to sage-edu@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-edu?hl=en -~----------~----~----~----~------~----~------~--~---
