Synaptory Chaos Explorer is a GPU-accelerated web application for real-time exploration of chaotic mathematical structures: Mandelbrot and Julia sets, the Riemann Zeta function, and the Rössler strange attractor. Built with WebGL, it renders directly on your GPU for smooth zooming, panning, and rotation through infinite complexity.
The Mandelbrot set reveals infinitely detailed structures at every scale. As you zoom deeper, discover spirals, seahorse valleys, and intricate self-similar patterns emerging from z = z² + c. Each boundary point corresponds to a unique Julia set, both explorable in real-time. Julia dives animate through parameter space, creating mesmerizing transitions between fractal forms.
The Riemann Zeta function mode visualizes one of mathematics' most important objects using domain coloring. Explore the critical line at Re(s) = 1/2 where non-trivial zeros are believed to lie—the famous Riemann Hypothesis. Features include: critical line overlay, zeta path spiral showing ζ(½+it) trajectory, analytic continuation toggle, and 25+ curated points of interest including trivial zeros, non-trivial zeros, Gram points, and historical milestones. Multiple shader algorithms available: Borwein, Riemann-Siegel, Double Precision, and Dirichlet Eta. Take the guided Zeta Tour with atmospheric music through critical line zeros.
The Rössler Attractor mode visualizes this classic 3D strange attractor discovered by Otto Rössler in 1976. Adjust parameters a (spiral tightness), b (z-axis coupling), and c (chaos level) in real-time. Render up to 15,000 iterations with customizable RGB color frequencies.
Navigate with mouse: scroll to zoom, drag to pan, double-click to center, right-drag to rotate. Touch controls: pinch to zoom, drag to pan, two fingers to rotate. Choose from curated views and color palettes. Save favorites locally, capture screenshots, and share coordinates via URL.
Synaptory Chaos Explorer is free and open-source under the MIT license. Visit the fractal gallery for curated screenshots, read the documentation, or explore the source code on GitHub.