A bidimensional fern computed by means of an 'Iterated Function System' -IFS- [Une fougère bidimensionnelle obtenue à l'aide de la méthode des 'Iterated Function Systems' -IFS-].
A bidimensional fern computed by means of an 'Iterated Function System' -IFS- [Une fougère bidimensionnelle obtenue à l'aide de la méthode des 'Iterated Function Systems' -IFS-].
A = {0,0,0} (displayed as a bigger Red sphere)
B = {1,0,0} (displayed as a bigger Green sphere)
(by the way, one point is enough for this iterative process...).
Then, the coordinates of these two points are iteratively transformed using
one of the four following linear transformations chosen randomly (each one with a different probability)
at each step:
/ \ / \ / \ / \
| X(i+1) | | +0.00 +0.00 0 | | X(i) | | +0.00 |
| | | | | | | |
| Y(i+1) | = | +0.00 +0.16 0 |.| Y(i) | + | +0.00 | probability=0.01
| | | | | | | |
| Z(i+1) | | 0 0 0 | | Z(i) | | 0 |
\ / \ / \ / \ /
/ \ / \ / \ / \
| X(i+1) | | +0.20 -0.26 0 | | X(i) | | +0.00 |
| | | | | | | |
| Y(i+1) | = | +0.23 +0.22 0 |.| Y(i) | + | +1.60 | probability=0.07
| | | | | | | |
| Z(i+1) | | 0 0 0 | | Z(i) | | 0 |
\ / \ / \ / \ /
/ \ / \ / \ / \
| X(i+1) | | -0.15 +0.28 0 | | X(i) | | +0.00 |
| | | | | | | |
| Y(i+1) | = | +0.26 +0.24 0 |.| Y(i) | + | +0.44 | probability=0.07
| | | | | | | |
| Z(i+1) | | 0 0 0 | | Z(i) | | 0 |
\ / \ / \ / \ /
/ \ / \ / \ / \
| X(i+1) | | +0.85 +0.04 0 | | X(i) | | +0.00 |
| | | | | | | |
| Y(i+1) | = | -0.04 +0.85 0 |.| Y(i) | + | +1.60 | probability=0.85
| | | | | | | |
| Z(i+1) | | 0 0 0 | | Z(i) | | 0 |
\ / \ / \ / \ /
Each point {X(i+1),Y(i+1),Z(i+1)} is displayed as a little sphere having the
color of the initial point {X(0),Y(0),Z(0)} (Red for A and Green for B).
