Vertical Initialization Reimagined: The Surprising Effects of Layered Rule Application

I had explored vertical streaks of initial cells in cellular automata, but the results were not very clear, as they looked similar to using a single initial point in the middle. However, with the layered application of cellular automata rules, a surprise emerged: new patterns appeared that weren’t present before.

Mathematically speaking, when I initialized the vertical streak of initial cells during standard rule generation, all initial points were already part of the grid. With layered rule generation, rules are applied one at a time. When combined with a multi-color palette, the results are captivating.

I will first show and compare the results after applying Rule 26 both with and without layered rule application.

Rule 26

Rule 26 of the 1D cellular automata with multiple colors and use of gradients

Rule 26 of the 1D cellular automata with layered rule generation and multiple colors

As you can clearly see, the image without layered rule application generates a pattern similar to what would be produced by a single initial cell in the top line of the cellular automata grid. However, in the second case with layered rule application, the vertical streak of initial points in the top middle produces distinctly new patterns.

I will explore some more interesting rules.

Rule 30

Rule 30 of the 1D cellular automata with layered rule generation and multiple colors

Rule 30 of the 1D cellular automata with layered rule generation and multiple colors

Rule 45

Rule 45 of the 1D cellular automata with layered rule generation and multiple colors

Rule 45 of the 1D cellular automata with layered rule generation and multiple colors

Rule 54

Rule 54 of the 1D cellular automata with layered rule generation and multiple colors

Rule 54 of the 1D cellular automata with layered rule generation and multiple colors

Rule 57

Rule 57 of the 1D cellular automata with layered rule generation and multiple colors

Rule 57 of the 1D cellular automata with layered rule generation and multiple colors

Rule 60

Rule 60 of the 1D cellular automata with layered rule generation and multiple colors

Rule 60 of the 1D cellular automata with layered rule generation and multiple colors

Rule 73

Rule 73 of the 1D cellular automata with layered rule generation and multiple colors

Rule 73 of the 1D cellular automata with layered rule generation and multiple colors

Rule 105

Rule 105 of the 1D cellular automata with layered rule generation and multiple colors

Rule 105 of the 1D cellular automata with layered rule generation and multiple colors

Rule 109

Rule 109 of the 1D cellular automata with layered rule generation and multiple colors

Rule 109 of the 1D cellular automata with layered rule generation and multiple colors

Rule 126

Rule 126 of the 1D cellular automata with layered rule generation and multiple colors

Rule 126 of the 1D cellular automata with layered rule generation and multiple colors

Rule 129

Rule 129 of the 1D cellular automata with layered rule generation and multiple colors

Rule 129 of the 1D cellular automata with layered rule generation and multiple colors

Rule 182

Rule 182 of the 1D cellular automata with layered rule generation and multiple colors

Rule 182 of the 1D cellular automata with layered rule generation and multiple colors

Rule 254

Rule 254 of the 1D cellular automata with layered rule generation and multiple colors

Rule 254 of the 1D cellular automata with layered rule generation and multiple colors

I loved the results from Rule 73. I feel that it is entirely a new pattern.

Written by Iohannes — John Samuel.