The Math-Problems Journey

Welcome to the Math-Problems Journey.

This repository is not just a collection of code snippets; it is a structured exploration of computational mathematics. Whether you are a student, a researcher, or just a curious programmer, this guide will help you navigate the complex systems contained within.

Why a Journey?

Mathematics and computer science are deeply interconnected. To truly understand concepts like Evolutionary Dynamics or Deterministic Chaos, you must first understand the fundamental algorithms that make simulating them possible.

We have structured this repository into four distinct stages. We recommend exploring them in order:

1

Stage 1

The Foundations

Before building complex simulations, you need the basic mathematical building blocks.

🚀 Getting Started

Learn how to setup, run, and execute the interactive code in this repository.

🔢 Number Theory

Explore prime numbers, factorization, modular arithmetic, and proofs in code.

📈 Equations Field

Solve linear/non-linear systems and plot mathematical equations dynamically.

2

Stage 2

Algorithms & Logic

Here, we apply optimized logic to solve complex, bounded computational problems.

📊 Sorting Visuals

Observe and compare how computers sort arrays and organize datasets visually.

🦇 Unique Algorithms

Bio-inspired heuristics like the Bat Searching and Firefly algorithms.

🔐 Security Algos

Delve into modern cryptography, ciphers, hashing, and security analyses.

🗂️ Sparse Matrix

Handle massive, mostly-empty multi-dimensional arrays with specialized libraries.

3

Stage 3

The Edge of Chaos

We move beyond predictable logic into the continuous, dynamic systems of determinism and chaos.

🌀 Math Chaos

Explore the Lorenz Attractor, attractors, and how small initial shifts trigger vast system splits.

❄️ Mandelbrot Fractals

Render and zoom infinitely into complex fractal geometries and mathematical coloring routines.

4

Stage 4

Simulating Life

The final frontier. Combining computation and geometry to simulate biology, physics, and evolution.

🕶️ PySpace Ray-Marching

Observe advanced 3D shaders, signed distance fields, and ray-marching logic.

🧬 GenePool Evolution

Watch autonomous, swimming creatures learn to move, feed, and reproduce over generations.

🦠 Particle Life

Observe colored particles forming cellular systems based on simple physics attraction rules.

🪐 Lenia Cellular Automata

Witness continuous cellular automata generating organic, self-organizing digital lifelike patterns.

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Ready?

Pick a stage from the sidebar on the left, or head straight to Stage 1: Getting Started to begin!