Core Features: Nine Scene Categories
Dive into the soul of MathArt and understand the mathematical engines behind stunning visual wonders. Each scene has its own dedicated page for deep reading and quick navigation.
🏗️ Surfaces & Geometry
From smooth parametric surfaces to organically blending implicit surfaces — explore the ever-changing three-dimensional geometries of mathematics.
Parametric Surface — The Beauty of Geometric Structure & Topology Define 3D surfaces through parametric equations , with dual render modes: particle point clouds and mesh surfaces. From spheres and toruses to Möbius strips and cornucopias, sculpt every contour with mathematical formulas.
Implicit Surface — Organically Fusing Isosurfaces Define 3D forms through scalar fields , inherently possessing the concept of "volume" — multiple implicit objects naturally blend when brought close together, forming liquid-like or organic morphologies (the famous "metaball" effect).
🌀 Chaos & Dynamical Systems
From differential equations of strange attractors to iterated maps and rotational symmetries — chaotic systems hold infinite visual surprises.
Strange Attractor — Visual Expression of Chaotic Systems Simulate particle trajectories driven by differential equations in 3D space, creating complex organic structures that reveal the "shape of chaos." From the butterfly-like Lorenz attractor to the spiral Aizawa attractor, each equation system conceals profound mathematical beauty.
Map Attractor — High-Density Visual Art from Discrete Maps Transform iterated maps (such as Clifford and Peter de Jong attractors) into high-density visual art. Leverages GPU-parallel iteration of hundreds of thousands of particles, using density accumulation and tone mapping to create images of extraordinary visual refinement.
Symmetry Chaos — The Symphony of Symmetry & Chaos Based on the seminal work of Michael Field and Martin Golubitsky, this scene forces rotational symmetry constraints into chaotic systems, generating attractor images with precise symmetric structures — from shield and cloak to pinwheel patterns.
🔍 Fractals & Recursion
From the classic Mandelbrot set to elegant spirographs, fractals reveal the beauty of infinite self-similarity.
Fractal — Recursion & Infinite Detail of Fractals High-performance GPU Fragment Shader rendering with 10 built-in fractal formulas, 10 coloring algorithms, and perturbation-driven ultra-deep zoom. From the classic Mandelbrot set to the unique Spiral Septagon, explore boundless complexity.
Spirograph — Mathematical Beauty & Geometric Rhythm A digital recreation of the classic mathematical drawing tool — combining gears and circles to create exquisite geometric patterns based on roulette curves. Adjust radius ratios and pen positions to generate infinite unique designs.
🖌️ Textures & Coloring
From the natural flow fields of Perlin noise to the complex-function visualization of domain coloring — reveal the invisible structures of mathematics.
Perlin Noise — Natural Textures & Flow Field Aesthetics Based on Ken Perlin's gradient noise algorithm, drive particle motion through 2D noise fields to create silk-like waves, nebula-like swirls, and circuit-like geometric textures. Supports dual rendering engines: CPU particle system and GPU shader.
Domain Coloring — A Visual Window into Complex Functions A classic method for visualizing complex functions — color every point on the complex plane, making core concepts of complex analysis such as zeros, poles, and branch points visible at a glance. From Riemann conformal mappings to fractal exploration, see the full picture of the complex world.
🎉 Ready to dive deeper? Now that you've mastered these core features, try defining your own mathematical formula. See the Advanced Customization Guide (coming soon).