fractals

`fernfale` (n) — Function

4 contractive maps, the probability to choice a transformation must be related with the contraction ratio. Argument n must be great enough, 10000 or greater.

Example:

(%i1) load("fractals")$
(%i2) n: 10000$
(%i3) plot2d([discrete,fernfale(n)], [style,dots])$

`hilbertmap` (nn) — Function

Hilbert map. Argument nn must be small (5, for example). Maxima can crash if nn is 7 or greater.

Example:

(%i1) load("fractals")$
(%i2) plot2d([discrete,hilbertmap(6)])$

`julia_parameter` — Variable

Default value: %i

Complex parameter for Julia fractals. Its default value is %i; we suggest the values -.745+%i*.113002, -.39054-%i*.58679, -.15652+%i*1.03225, -.194+%i*.6557 and .011031-%i*.67037.

`julia_set` (x, y) — Function

Julia sets.

This program is time consuming because it must make a lot of operations; the computing time is also related with the number of grid points.

Example:

(%i1) load("fractals")$
(%i2) plot3d (julia_set, [x, -2, 1], [y, -1.5, 1.5],
                [gnuplot_preamble, "set view map"],
                [gnuplot_pm3d, true],
                [grid, 150, 150])$

`julia_sin` (x, y) — Function

While function julia_set implements the transformation julia_parameter+z^2, function julia_sin implements julia_parameter*sin(z). See source code for more details.

This program runs slowly because it calculates a lot of sines.

Example:

This program is time consuming because it must make a lot of operations; the computing time is also related with the number of grid points.

(%i1) load("fractals")$
(%i2) julia_parameter:1+.1*%i$
(%i3) plot3d (julia_sin, [x, -2, 2], [y, -3, 3], 
                [gnuplot_preamble, "set view map"],
                [gnuplot_pm3d, true],
                [grid, 150, 150])$

`mandelbrot_set` (x, y) — Function

Mandelbrot set.

Example:

This program is time consuming because it must make a lot of operations; the computing time is also related with the number of grid points.

(%i1) load("fractals")$
(%i2) plot3d (mandelbrot_set, [x, -2.5, 1], [y, -1.5, 1.5],
                [gnuplot_preamble, "set view map"],
                [gnuplot_pm3d, true],
                [grid, 150, 150])$

`sierpinskiale` (n) — Function

Sierpinski Triangle: 3 contractive maps; .5 contraction constant and translations; all maps have the same contraction ratio. Argument n must be great enough, 10000 or greater.

Example:

(%i1) load("fractals")$
(%i2) n: 10000$
(%i3) plot2d([discrete,sierpinskiale(n)], [style,dots])$

`sierpinskimap` (nn) — Function

Sierpinski map. Argument nn must be small (5, for example). Maxima can crash if nn is 7 or greater.

Example:

(%i1) load("fractals")$
(%i2) plot2d([discrete,sierpinskimap(6)])$

`snowmap` (ent, nn) — Function

Koch snowflake sets. Function snowmap plots the snow Koch map over the vertex of an initial closed polygonal, in the complex plane. Here
the orientation of the polygon is important. Argument nn is the number of recursive applications of Koch transformation; nn must be small (5 or 6).

Examples:

(%i1) load("fractals")$
(%i2) plot2d([discrete,
              snowmap([1,exp(%i*%pi*2/3),exp(-%i*%pi*2/3),1],4)])$
(%i3) plot2d([discrete,
              snowmap([1,exp(-%i*%pi*2/3),exp(%i*%pi*2/3),1],4)])$
(%i4) plot2d([discrete, snowmap([0,1,1+%i,%i,0],4)])$
(%i5) plot2d([discrete, snowmap([0,%i,1+%i,1,0],4)])$

`treefale` (n) — Function

3 contractive maps all with the same contraction ratio. Argument n must be great enough, 10000 or greater.

Example:

(%i1) load("fractals")$
(%i2) n: 10000$
(%i3) plot2d([discrete,treefale(n)], [style,dots])$

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