Skip to main content

Exploring Mobile Automata with Non-Local Rules

This summer, I had the incredible opportunity to attend the Wolfram High School Summer Research Program. Interested in ruliology, I focused my project on mobile automata, a type of simple program similar to cellular automata.

Mobile Automata with Non-Local Rules

In cellular automata, all cells update in parallel according to a set of rules, whereas mobile automata feature a single active cell that updates at each iteration. The rules for mobile automata dictate the new state of the active cell and its movement. These rules consider the states of the active cell and its immediate neighbors, determining the new color of the active cell and whether it moves to the left or right.


Traditionally, mobile automata involve the active cell interacting with its immediate left and right neighbors. However, in my project, I explored the effects of non-local interactions, where the dependent cells are farther away from the active cell. For instance, I examined scenarios where the dependent cells were two cells to the left and three cells to the right of the active cell.


Mobile automata can also have rules that increase the number of active cells. By implementing non-local rules in those types of rules as well, I was able to find immense complexity from a simple set of rules. Here is a picture from my project, where the black dots symbolize the active cells and the numbers on top represent the dependent cell ranges.

Some Possible Philosophical Implications


Exploring mobile automata with non-local rules opens up fascinating philosophical questions about the nature of complexity and emergence. One key question is how simple rules can lead to highly complex behaviors. This ties into the broader philosophical debate about reductionism and emergence. Can the behavior of a complex system be fully understood by examining its parts, or does the system exhibit properties that are not present in its individual components?


Furthermore, this research touches on the concept of interconnectedness. In mobile automata with non-local rules, the state of the active cell depends on cells that are not immediately adjacent, suggesting that even distant elements in a system can have significant impacts on its behavior. This idea resonates with philosophical discussions about the interconnectedness of all things in the universe, where actions in one part of a system can have far-reaching effects. This could also have implications in nonlocality seen in systems in quantum mechanics.


For More Information


For a more in-depth dive into mobile automata with non-local rules, you can check out my computational essay in the form of a Wolfram Community post here: https://community.wolfram.com/groups/-/m/t/3214519?p_p_auth=z3DG3Bp8


This essay was the final product of the whole program so it includes all of my findings and complexity regarding mobile automata with non-local rules.

Comments

Popular posts from this blog

What is Nothing?

What does it mean for nothing to exist? At first, the question sounds simple, even a little silly. But both scientists and philosophers have struggled with the idea of "nothing" for centuries. Is empty space truly empty? Can “nothingness” actually exist, or is it just a word we use when we don’t know what else to say? In this post, we’ll explore how science and philosophy look at the idea of nothingness—from ancient views of the void to modern physics and quantum theory—and ask whether nothing is ever really… nothing. Nothing in Philosophy: The Ancient Void Philosophers have debated the concept of nothingness for thousands of years. In ancient Greece, thinkers like Parmenides argued that “nothing” cannot exist at all. To him, the very act of thinking or speaking about “nothing” meant that it was something , which made the idea of true nothingness impossible. On the other hand, Democritus , who imagined the world as made of tiny atoms, believed that atoms moved through an ...

Does String Theory Count as Science?

String theory is one of the most ambitious and imaginative ideas in modern physics. It aims to do something no other theory has done: unify all the fundamental forces of nature ( gravity, electromagnetism, the strong nuclear force, and the weak nuclear force) into a single framework. It replaces point-like particles with tiny vibrating strings , whose vibrations determine the type of particle you observe. But despite its promise, string theory is also one of the most controversial theories, because right now, it can't be tested . So this leads to a deep philosophical question: If a theory explains everything but can’t be tested, does it still count as science? In string theory, fundamental particles like electrons, protons, and quarks are represented as tiny vibrating strings. The type of particle is determined by the string’s vibrational pattern, similar to how different notes come from the same guitar string. Tripathi, A. (2024, March 24). String Theory: Dimensional Implicatio...

The Anthropic Principle and Fine-Tuning Debates

When we look at the universe, it seems almost perfectly set up for the existence of life. Many of the laws of physics work in just the right way to allow stars to form, planets to exist, and complex life to develop. This idea that our universe is “fine-tuned” for life has led to many discussions about what it really means. Some believe it might be just a lucky accident, while others think there could be a deeper reason. These debates bring us to the Anthropic Principle, which is a way of explaining why we see the universe as so well suited for living things. The Puzzle of Fine-Tuning Scientists have found that if certain physical laws or constants—such as the strength of gravity or the charge on the electron—were slightly different, stars might not form or atoms might not stay together. If that happened, life as we know it would not be possible. The universe’s seeming “perfect fit” for life is sometimes called the “fine-tuning” problem, because it is as though these constants were set ...