IFS Chaos Text

Written by Paul Bourke
January 2002

Contributed by Earl Glynn (Original source unknown)


The following is a rather unusual example of an iterated function system (IFS) that involves choosing at random one of 19 transformations of the form

xn+1 = a xn + b yn + e
yn+1 = c xn + d yn + f

A zoom into the top portion of the "A", shown in blue above, shows that it is indeed made up of smaller versions of the word "chaos".

And to labour the point, the following is a further zoom into the "A", shown in blue above.

The parameter table:

    a           b           c            d            e         f
    0           0.053      -0.429        0           -7.083     5.43
    0.143       0           0           -0.053       -5.619     8.513
    0.143       0           0            0.083       -5.619     2.057
    0           0.053       0.429        0           -3.952     5.43
    0.119       0           0            0.053       -2.555     4.536
   -0.0123806  -0.0649723   0.423819     0.00189797  -1.226     5.235
    0.0852291   0.0506328   0.420449     0.0156626   -0.421     4.569
    0.104432    0.00529117  0.0570516    0.0527352    0.976     8.113
   -0.00814186 -0.0417935   0.423922     0.00415972   1.934     5.37
    0.093       0           0            0.053        0.861     4.536
    0           0.053      -0.429        0            2.447     5.43
    0.119       0           0           -0.053        3.363     8.513
    0.119       0           0            0.053        3.363     1.487
    0           0.053       0.429        0            3.972     4.569
    0.123998   -0.00183957  0.000691208  0.0629731    6.275     7.716
    0           0.053       0.167        0            5.215     6.483
    0.071       0           0            0.053        6.279     5.298
    0          -0.053      -0.238        0            6.805     3.714
   -0.121       0           0            0.053        5.941     1.487