Chapter 3: The World of Simple Programs

Section 5: Substitution Systems

2D representations [of substitution systems]

Individual sequences from 1D substitution systems can be displayed in 2D by breaking them into a succession of rows. The pictures below show results for the substitution systems on page 83. In case (b), with rows chosen to be 2j elements in length, the leftmost column will always be identical to the beginning of the sequence, and in addition every interior element will be black exactly when the cell at the top of its column has the same color as the one at the beginning of its row. In case (c), stripes appear at angles related to GoldenRatio.

Image Source Notebooks:

From Stephen Wolfram: A New Kind of Science [citation]