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# Ensemble de Mandelbrot

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Visualisation de l'ensemble de Mandelbrot

Proc?dure tr?s lente : utilisation de evalf

 > mandelbrot1:=proc(c,maxit) local j,mc,z; mc:=max(2,abs(c)); z:=0; for j from 0 to maxit      while abs (z) < mc do        z:=evalf(z^2+c);    od; evalf(sqrt(j-1)); end;    (1.1.1)

 > mandelbrot1(5/8+I/8,50); (1)

 > restart:

Proc?dure rapide : utilisation de evalhf

 > mandelbrot2:=proc(a,b) local j,mc2,x,y,x_i,y_i; mc2:=max(4,a^2+b^2); x:=0; y:=0; for j from 0 to maxit      while  evalhf(x^2+y^2) < mc2 do        x_i:=evalhf(x^2-y^2+a);        y_i:=evalhf(2*x*y+b);        x:=x_i;        y:=y_i;            od; evalhf((j-1)^(1/2)); end;        (2.1)

 > maxit:=100:

 > mandelbrot2(5/8,1/8); (2.2)

Proc?dure pour faire un "zoom"  sur l'ensemble de Mandelbrot

 > zoomM:=proc(xc,yc,larg,mx,nbpix) local xmin,xmax,ymin,ymax; global maxit; maxit:=mx; xmin:=xc-larg/2; xmax:=xc+larg/2; ymin:=yc-larg/2; ymax:=yc+larg/2; plot3d(0,xmin..xmax,ymin..ymax,numpoints=nbpix^2,style=patchnogrid,orientation=[-90,0],scaling=constrained,color=mandelbrot2,axes=normal); end;          (2.3)

 > zoomM(-0.5,0,2.5,200,300); > zoomM(-1.356,0.0686,.0025,400,300); Legal Notice: The copyright for this application is owned by the author(s). Neither Maplesoft nor the author are responsible for any errors contained within and are not liable for any damages resulting from the use of this material. This application is intended for non-commercial, non-profit use only. Contact the author for permission if you wish to use this application in for-profit activities. 