48.2 Definitions for IFS fractals

Some fractals can be generated by iterative applications of contractive affine transformations in a random way; see Hoggar S. G., "Mathematics for computer graphics", Cambridge University Press 1994.

We define a list with several contractive affine transformations, and we randomly select the transformation in a recursive way. The probability of the choice of a transformation must be related with the contraction ratio.

You can change the transformations and find another fractal

Function: sierpinskiale (n) ¶

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

Example:

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

Function: treefale (n) ¶

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

Example:

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

Function: fernfale (n) ¶

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

Example:

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