Create fractals IFS ( iterated function systems ) 
with MRCM (Multiple Reduction Copy Machine ) 

We define transforms by drawing image of work's canvas ( a square ). 
As transforms are affinities this image must be a parallelogram or particulary square, rectangle .....
For a dilatation, we have a square with same orientation ( first point is left top point ).
If we rotate square, we add a rotation and we have a similiraty. If we change orientation, we add a reflection ....
If we have a rectangle, transform is affinity with perpendicular axis. Parallelogram give most ordinary transform, affinity.

We draw polylines, one or more, which are transformed. If we choose 1 as level, polyline is transformed by each. With level 2, we have all composed transforms, if we have defined 3 transforms, we have 9, 27, 81 .... composed transforms at level 2, 3, 4 .....

June 2006
New version for Firefox and Opera

* all features of SVGDraw
* load existing work, save work and IFS as svg
* see animated building of Von Koch's curve
* enter affinity by mouse or by values


Adobe's plugin ( versions 3.03 and 6 beta)
Opera 9 beta 2
* No printing of IFS
* Actually problem to retrieve paths and no IFS ....
Firefox 1.5 
* No pictures and text in widgets
* No animation to see IFS's building
Batik 1.6 
* No refresh for tiles drawing  
* Cannot save work - node -> string and postURL emulation
* No animation to see IFS's building

Try application on line

Load application with examples and help in Zip file ( 709 ko )
( need Apache and PHP to run in local )

Fractals for Classroom de Peitgen, Jürgens et Saupe    2 tomes  ( Springer Verlag )