Bittensor Subnet 36:Web Agents

Cellular automata are mathematical systems that show how simple rules can create complex, emergent behaviors. Rule 30, introduced by Stephen Wolfram, is particularly intriguing because it produces seemingly random and unpredictable patterns despite its simplicity, challenging our understanding of complexity and computation.

Here’s how Rule 30 operates:

The automaton functions on a grid where each cell is either alive (white) or dead (black). Each cell’s state in the next row is determined by its own state and that of its two immediate neighbors above.

Starting with a single black cell, Rule 30 generates a pattern that:

• Appears random along its center column
• Forms complex, asymmetric triangular structures
• Avoids periodicity even after a billion steps

The name “Rule 30” comes from converting these output states to binary (00011110), which equals 30 in decimal.

Wolfram posed three fundamental questions about Rule 30 that remain unanswered:

• Pattern Periodicity: Does the center column always remain non-periodic?
• Distribution Properties: Does each color of cell occur on average equally often in the center column?
• Computational Complexity: Does computing the nth cell of the center column require at least O(n) computational effort?

These questions lie at the core of complexity science and carry significant implications across various fields:

• Cryptography: Understanding pattern generation for secure systems
• Machine Learning: Training models using data from emergent behaviors
• Complex Systems: Predicting behavior in chaotic environments.

Recent studies show that transformer models trained on cellular automata data can perform better on complex tasks. By generating an extensive dataset from Rule 30 computations, this project opens up new paths for AI model training while also addressing Wolfram’s key questions about emergent complexity.

Overview of Miner and Validator Functions

Their subnet coordinates validators and miners to collaboratively generate and analyze the first trillion values in Rule 30’s center column, working toward answers to these fundamental questions.

Miners: Responsible for generating Rule 30 patterns by computing assigned row ranges of the cellular automaton. Using optimized algorithms and parallel processing, miners calculate these pattern segments to contribute to the target of analyzing a trillion steps in Rule 30’s center column.

Validators: Distribute computational tasks and verify miner outputs. Given the deterministic nature of Rule 30, each computation has only one correct answer, making validation efficient. Validators confirm accuracy, assess response time, and reward miners based on performance.