Category: Kamtori

This fractal is the byproduct of various efforts to find an answer to the question whether our Solar System is stable or not. It is named after Russian mathematician A.N. Kolmogorov who developed a theory predicting the form and stability of the orbits of the planets. The theory was independently confirmed by Mr. Kolmogorov's student, V.I. Arnold and the German mathematician J. Moser (hence the name: Kolmogorov, Arnold, and Moser).

> restart:

> kamtorus := proc(angle, step, ende, points)
> # written by Alexander F. Walz
> # Version 1.0 - May 31, 1996
> # Version 1.1 - May 23, 1999 - optimized, 4 times faster than v 1.0
>    local x, xold, y, orbit, pts, ptscounter, n;
>    pts := table([]);
>    ptscounter := 0;
>    for orbit from 0 by step to ende do
>       x := orbit/3;
>       y := x;
>       to points while abs(x) < 10^38 and abs(y) < 10^38 do 
>          # to avoid violation of ranges
>          xold:=x;
>          x := evalhf(x*cos(angle) + (x^2-y)*sin(angle));
>          y := evalhf(xold*sin(angle) - (xold^2-y)*cos(angle));
>          ptscounter := ptscounter + 1;
>          pts[ptscounter] := [x, y];
>       od;  # end of to points
>    od; # of for orbit
>    [seq(pts[n], n=1 .. ptscounter)]
> end:

> plot(kamtorus(1.3, 0.05, 1.5, 200), style=point, symbol=POINT, 
>    axes=none, scaling=constrained);

MAPLE V FRACTALS KAM Torus #1.2 current as of May 23, 1999
Author: Alexander F. Walz, alexander.f.walz@t-online.de
Original file location: http://www.math.utsa.edu/mirrors/maple/mfrkam.htm