Welcome back to our ongoing exploration of cellular automata and their captivating world, one rule at a time. After illuminating the intriguing aspects of Rules 30 and 151, we turn our focus towards Rule 90—an intriguing highlight in the realm of cellular automata that endears itself to mathematicians and designers alike.
What is Rule 90?
Rule 90, with the binary representation 01011010, is one of the most interesting and simple rules in Stephen Wolfram's realm of cellular automata. This rule guides a cell's evolutionary journey based on its current state and its neighbouring cells' states.
Rule 90's Working Principle
Rule 90 operates as follows:
- If a cell and its neighbours are 10 or 01, the next state of the cell is 1.
- If a cell and its neighbours are 11, 00, the next state of the cell is 0.
This rule, though straightforward, when applied repeatedly across various generations, starts painting complex patterns that captivate the observer.
Fascinating Patterns of Rule 90
The fascinating aspect of Rule 90 is the symmetry it engenders. The patterns form triangles within triangles, creating a fractal-like design. The emerging design is known as the Sierpinski triangle, named after Polish mathematician Waclaw Sierpinski who described this mathematical construct.
This intricate, self-similar pattern—where every part reflects the whole—exemplifies elegance, simplicity, and unlimited complexity at once. The mind sees constant dichotomy—the simplicity of the rule against the sophistication of the pattern it forms.
Applications of Rule 90
Beyond its visual appeal, Rule 90 has practical applications as well. Rule 90 generates a sequence known to mathematicians as the Thue-Morse sequence, making it an interesting subject for mathematical research. Plus, it often finds a home in procedural generation in computer graphics, creating fascinating digital visuals and arts.
Wrapping up
Here at RuleThirty, we strive to shine a light on the beauty of mathematics, and Rule 90 is a prime example of how digital abstraction can materialize into stunning art. It perfectly captures the intricate ballet of simplicity and complexity, reminding us of the magic hidden in the depths of numbers and algorithms.
Our journey across the universe of cellular automata is far from over. There's more mathematical beauty to be unveiled and more captivating stories to narrate. Stay with us as we navigate this universe—one rule at a time. Remember, Rule 90 is just one small piece of the giant mathematical jigsaw puzzle!