Day 14 - Aizawa Attractor: The Spherical Chaos | Generative Math Art

Welcome to Day 14 of CM2A.
Code + Math = Art.

// THE VISUALIZATION
Today we explore the Aizawa Attractor, a chaotic dynamical system that forms a dense, spherical cloud of orbits.
This render is built as a multi-stage journey through the attractor:

INTRO – Birth of the Sphere
Side view: X vs (Z − 0.5), scaled to reveal the spherical shell structure.

TIME SERIES – x(t)
We map time t → X and the Aizawa x-coordinate → Y to show how the system oscillates over time.

TIME SERIES – z(t)
Plotting z(t) (shifted by −0.5) against time, highlighting vertical chaotic motion.

PHASE PLANE – x vs y
Classic phase portrait X = 1.7x, Y = 1.7y showing the swirling rotational structure.

3D PERSPECTIVE PROJECTION
An isometric-like projection using:
x_iso = (x − y)·cos(40°)
y_iso = z − 0.5 + (x + y)·sin(40°)
This flattens 3D chaos into a cinematic 2D viewpoint.

FINAL – The Aizawa Sphere
A full breathing “chaos sphere” view, using a subtle pulse term to make the attractor feel alive.

// THE MATH
Aizawa System:
dx/dt = (z − b)x − d·y
dy/dt = d·x + (z − b)y
dz/dt = c + a·z − z³/3 − (x² + y²)(1 + e·z) + f·z·x³

Parameters:
a = 0.95, b = 0.7, c = 0.6
d = 3.5, e = 0.25, f = 0.1

The CM2A Engine numerically integrates the system with small dt, then normalizes and scales (x, y, z) for each stage, adding a breathing pulse:
pulse = 0.95 + 0.05·sin(0.25t)

// THE ENGINE
Software: CM2A Custom Engine v1.0 (Python/CustomTkinter)
Render: Real-time generation
Resolution: 1080p @ 60fps

// ABOUT CM2A
Code + Math = Art.
We explore generative algorithms, physics simulations, and parametric equations.
No CGI tools. Just pure code.

// CONNECT
Created by Eng. Rizni Mohamed.
Subscribe for your daily dose of mathematical satisfaction.

#mathart #generativeart #python #satisfying #aizawaattractor #chaos #strangeattractor #creativecoding #CM2A