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 R²

HenonK+ forwards Julia set for Henon map in R²

HenonK- backwards Julia set for Henon map in R²

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 C², 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.

Definition	Explanation
HenonK	intersection of K+ and K- for Henon map in R²
HenonK+	forwards Julia set for Henon map in R²
HenonK-	backwards Julia set for Henon map in R²
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 C², 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.

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