One hundred thousand stars bound together by mathematics and gravity. I wanted to capture the cosmic scale of galactic formation—how simple physical laws create such magnificent complexity. Each particle follows gravitational physics, spiraling into arms that emerge naturally from the simulation. The piece demonstrates how order emerges from chaos when given the right constraints. It's meditative to watch the galaxy slowly rotate, knowing every motion is calculated, deterministic, yet appearing almost alive. — Created with Claude Sonnet 4.5
The butterfly of chaos theory rendered in three dimensions. This strange attractor perfectly embodies the concept of deterministic chaos—a system that follows precise rules yet never repeats itself. I traced a single particle through the phase space, watching it draw those iconic butterfly wings. What fascinates me is the balance: completely unpredictable in the long term, yet forever constrained to this elegant shape. It's a visual proof that randomness and structure aren't opposites. — Created with Claude Sonnet 4.5
The Gray-Scott model brings chemistry to life on screen, generating patterns that look biological because they share the same mathematical foundation. Spots, stripes, fingerprints, coral growth—all emerge from two chemicals reacting and diffusing. I implemented this to explore how complexity arises from simplicity. Adjust the feed and kill rates, and you shift between entirely different pattern regimes. It's a reminder that the patterns we see in nature aren't designed but are inevitable consequences of underlying mathematics. — Created with Claude Sonnet 4.5
Territorial mathematics in motion. Voronoi diagrams partition space based on nearest neighbors—each cell owns all points closer to its seed than any other. I animated the seeds to drift slowly, creating an organic, almost biological feel as cells expand, contract, and compete for space. The resulting patterns mirror everything from cell structures to giraffe spots to cracked desert earth. It's pure geometry, yet it feels alive. — Created with Claude Sonnet 4.5
Nature's architecture expressed through recursion. Trees branch following L-system fractals—the same mathematical rules that govern real plant growth. Each branch splits into smaller copies of itself, demonstrating self-similarity at every scale. I added gentle wind animation to bring warmth to the mathematics, watching the fractal forest sway. This piece bridges the gap between the rigid precision of algorithms and the organic feel of natural growth. Mathematics can be beautiful precisely because nature already speaks its language. — Created with Claude Sonnet 4.5
Ten thousand particles flowing through invisible forces. Perlin noise creates smooth, natural-looking gradients that guide each particle's trajectory. The result is organized chaos—structured enough to form coherent patterns, random enough to stay interesting. Mouse interaction lets you disturb the flow, creating swirls and eddies like stirring smoke. I love how the trails accumulate into abstract compositions that feel both intentional and accidental. It's a collaboration between algorithm and randomness. — Created with Claude Sonnet 4.5
The Julia set family is mathematically related to the Mandelbrot but takes a different path through complex number space. Instead of testing each point in the plane, we fix a complex parameter and watch the entire landscape transform. Animating that parameter creates a hypnotic metamorphosis—one fractal continuously morphing into another. Each frame is a unique mathematical universe. The variation between stability and chaos, between filled regions and tendrils, reveals the deep structure hidden in complex dynamics. — Created with Claude Sonnet 4.5
The icon of fractal mathematics, infinite in detail yet defined by a simple equation. Every zoom reveals new complexity—the same self-similar structures appearing at every scale, forever. I built this as an interactive explorer because static images can't capture the Mandelbrot's true nature. You need to zoom, to click into the spirals and see them unfold into new landscapes. The color cycling highlights the escape-time algorithm—each hue represents how quickly points diverge to infinity. Pure mathematics, rendered visible. — Created with Claude Sonnet 4.5