These pictures of the Mandlebrot set were plotted using Maple. The full Mandlebrot set is the dark pink image in the first image. The other images are closeups of the boundary. You should note that the Mandelbrot set contains multiple copies of itself.

     The Mandlebrot set is generated in the complex plane by the following iterative procedure: For each complex number c, generate a sequence as follows: square c and add to c, square the result and add to c, square the result and add to c, etc. The point is in the set if and only if the sequence remains bounded.

     The pictures below are done by generating numbers in each sequence until either 100 points are generated or the magnitude of the iterate exceeds 10. The colors outside the set are determined by how quickly the points get larger than 10. Maple is capable of doing complex number arithmetic, but the following program using real arithmetic runs much more quickly.

>	F:= proc(x,y) local Y,X,X1,C1,C2,N: X:=evalf(x): Y:=evalf(y): C1:=X:  C2:=Y: for N from 1 to 100 while X^2+Y^2<100 do   X1:=X:   X:=X^2-Y^2+C1:   Y:=2*X1*Y +C2: od: if X^2+Y^2<100 then 0 else N fi: end proc:

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gs:=300;

>	plot3d(F,-2.3..0.9,-1.35..1.35,shading=zhue,style=patchnogrid,orientation=[-90,0], grid=[gs,gs], lightmodel=light4);

>	plot3d(F, -1.8..-1.72, -0.04..0.04, shading=zhue, style=patchnogrid, orientation=[-90,0], grid=[gs,gs], lightmodel=light4);

>	plot3d(F, -.75..-.55, .3..0.5, shading=zhue, style=patchnogrid, orientation=[-90,0], grid=[gs,gs], lightmodel=light4);

>	plot3d(F, -.71..-.63, .42..0.5, shading=zhue, style=patchnogrid, orientation=[-90,0], grid=[gs,gs], lightmodel=light4);

>	plot3d(F, -.69..-.66, 0.44..0.47, shading=zhue, style=patchnogrid, orientation=[-90,0], grid=[gs,gs], lightmodel=light4);

>	plot3d(F, -.675..-.665, .453..0.463, shading=zhue, style=patchnogrid, orientation=[-90,0], grid=[gs,gs], lightmodel=light4);

>	plot3d(F, -.2..0, .9..1.1, shading=zhue, style=patchnogrid, orientation=[-90,0], grid=[gs,gs], lightmodel=light4);

>	plot3d(F, -.18..-.14, 1.015..1.055, shading=zhue, style=patchnogrid, orientation=[-90,0], grid=[gs,gs], lightmodel=light4);

>	plot3d(F, -1..-.7, 0..0.3, shading=zhue, style=patchnogrid, orientation=[-90,0], grid=[gs,gs], lightmodel=light4);

>	plot3d(F, -.9..-.85, .23..0.28, shading=zhue, style=patchnogrid, orientation=[-90,0], grid=[gs,gs], lightmodel=light4);

>	plot3d(F, -.88..-.87, .25..0.26, shading=zhue, style=patchnogrid, orientation=[-90,0], grid=[gs,gs], lightmodel=light4);

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