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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
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])$
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])$
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])$
Next: Definitions for complex fractals, Previous: Introduction to fractals, Up: fractals [Contents][Index]