FractalAsm Definition List
The following FractalAsm definitions were used to make some of the pictures on this website. FractalAsm requires a Power Macintosh or compatible in order to run. The archive contains the following definitions:
Definition | Explanation |
---|---|
HenonK | intersection of K+ and K- for Henon map in R^{2} |
HenonK+ | forwards Julia set for Henon map in R^{2} |
HenonK- | backwards Julia set for Henon map in R^{2} |
HenonSiegel | Shows Siegel Balls of a Henon map: the eigenvalues (multiplicators are parameters m1 and m2) should be of norm 1. The 's' parameter determines the slope of the complex slice being displayed. |
HenonSiegel-vary-m | used for making movies of HenonSiegel |
HenonSiegel-vary-s | used for making movies of HenonSiegel |
Henon_Unstable_Manifold | Plots forwards Julia set on Unstable Manifold; uses ParamComp to compute fixed point and its eigenvalue |
Newton M-Period 3 | Basins of attraction of Newton's Method for locating the period-3 centers of the Mandelbrot set |
Newton M-Period 5 | same as above, but period-5 centers |
Newton M-Period 8 | same as above, but period-8 centers |
Newtoncasea=1 | Newton's method to find the intersection of two quadratic curves in C^{2}, one of which is degenerate. Roots are at (0,0), (0,1), (1,0) and (1,b). This definition colors a slice Re(x)= 1/2, and colors the basins of the roots of Newton's Method in this slice (not the same as the original 4 roots). |
Newtoncasea=1,parabola | Same Newton's method, but the parabola containing the 4 original roots is displayed. |
Newtoncasea=1,vary | used for making movies of Newtoncasea=1 |
Newtoncasea=1space | Same degenerate case but we can vary Re x. |
NewtonOnLines | ?? |
Rat2,per3 | Iteration of rational maps with an attracting cycle of period 3; 3 parts of basin colored separately (use a color set with different colors for Roots 1..3) |
Rat2,per3,makeJ | parameter space for the above |
Rat2,per3,makeJ,infinity | ?? |
Sqrt Polynomial2 | Iteration of a polynomial with two quadratic-attracting points, which is used to compute square roots. |
Sqrt Polynomial3 | Iteration of a polynomial with two cubic-attracting points, which is used to compute square roots. |