Growth in 1D Substitution Systems with Two Colors and Up to One Neighbor

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

Substitution systems whose rules depend on the color of a single element and on the color of the next neighbor produce an unbalanced rate of growth and disappearance. If the rate of disappearances is too large, then almost any pattern will quickly die out, and if there are too few disappearances, then most patterns will grow exponentially or sub-exponentially. This model is a derivation of the neighbor-dependent model, allowing growth from one single cell. You can explore 117649 rules of this kind.

Contributed by: Enrique Barrajon (August 2011)
Suggested and revised by: Paul-Jean Letourneau
Open content licensed under CC BY-NC-SA


Snapshots


Details

As an example, rule 111715 produces sub-exponential growth starting from a white cell. The pattern of growth is exponential when starting from two white cells, but reverts to sub-exponential when a black cell is in between them.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send