Ensemble de Mandelbrot 

by Prof. Samir KADDOURI  

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)

 

(1)

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);

 

 

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