Fractal Patterns from a Substitution Blueprint

iterations

0

1

2

3

4

5

kernel size

2

3

4

5

kernel

clear kernel

random kernel

area now:

0.45679

limiting area:

3

7

The "kernel" is a blueprint for constructing a self-similar figure. At iteration

n

, a new image is produced based on the kernel in the following ways:

• If the entry in the kernel corresponding to a segment of the image is black, that segment is colored black.

• If its corresponding entry is white, the segment is colored white.

• If its corresponding entry is gray, the segment is replaced with a scaled copy of the entire image as it appeared at iteration

n-1

.

Under the buttons on the left, the area of the black portion of the figure is given, both as of the current iteration and in the limit. For best results, set the controls from top to bottom. Clear kernel for a new figure.