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Penrose Tiling

Implementing Penrose tilings - aperiodic patterns that never repeat regardless of how far they're extended. My implementation features:

L-System based pattern generation for fractal-like growth
Interactive click-and-drag controls for pattern manipulation
Custom shader-based rendering for optimal visual output
Smooth animation system to visualize pattern growth

The core algorithm uses L-System substitution rules to generate these complex geometric patterns. Each iteration creates increasingly detailed self-similar structures while maintaining the fundamental aperiodic property.

Reference implementation: https://www.forritun.dev/projects/penrose

Chladni Patterns

Digital recreation of Chladni figures - the geometric patterns that emerge when vibrating a plate at specific resonant frequencies. The implementation includes:

Real-time pattern generation via GLSL fragment shaders for performance
Parameter sliders to adjust n and m modal values for different pattern types
Customizable color mapping and opacity controls
Time-based evolution with animated transitions between states

The technical approach involves solving the wave equation for a vibrating plate and visualizing the nodal lines (where amplitude = 0) using shader-based rendering. The standing wave patterns are computed based on eigenfunction solutions.

Reference implementation: https://www.forritun.dev/projects/chladni

Double Pendulum

A double pendulum simulation that demonstrates chaotic dynamics in a simple mechanical system. Features include:

Accurate physics simulation based on Lagrangian mechanics
Interactive mouse control for initial conditions
Motion trail visualization with temporal fading
Color-coded component rendering for tracking movement
Responsive design that adapts to viewport dimensions

The implementation solves the coupled differential equations using fourth-order Runge-Kutta numerical integration. This provides accuracy while maintaining real-time performance across devices.

Reference implementation: https://www.forritun.dev/projects/pendulum

Spirograph

Digital implementation of the classical spirograph drawing toy, generating hypotrochoid and epitrochoid curves. The tool offers:

Adjustable parameters for gear ratios, hole positions, and rotation rates
Real-time rendering of parametric curves
Custom color selection for stroke and background elements
One-click pattern saving functionality
Multi-touch support for tablet interactions

The mathematical model uses parametric equations to trace the path of a point on a circle rolling around the inside or outside of another circle. These equations generate continuous curves with fascinating symmetry properties.

Reference implementation: https://www.forritun.dev/projects/spirograph

Mandelbrot Set

Interactive explorer for the Mandelbrot set fractal with advanced rendering capabilities. Key features:

GPU-accelerated zooming and panning for smooth navigation
Configurable color mapping with customizable gradient palettes
Optimized escape-time algorithm with early bailout conditions
Variable iteration depth control for exploring deeper structures

The rendering engine uses complex number arithmetic to iterate the function z = z² + c, tracking how quickly each point escapes a boundary radius (or if it remains bounded). The iteration count determines color mapping for visualizing the fractal boundary.

Reference implementation: https://www.forritun.dev/projects/mandelbrot

Conway's Game of Life

Implementation of Conway's cellular automaton with an expanded feature set. The simulation includes:

Custom pattern drawing and preset template library
Cell age visualization using color gradients
Toroidal grid implementation with edge wrapping
Comprehensive playback controls (pause, step, reset)

The core logic follows Conway's four rules: underpopulation, survival, overpopulation, and reproduction. Despite this simple ruleset, the simulation exhibits emergent complexity capable of universal computation.