mathematics

Mathematics

The language of the universe — from prime numbers and fractals to probability and the surprising patterns hidden in abstract structures.

mathematicsfractalsprobabilityprime numbersgolden ratioFourierstatistics

Mathematics is the foundation of all science. It reveals patterns that govern everything from the spiral of galaxies to the growth of populations, from the security of your bank account to the unpredictability of weather. These simulations let you explore mathematical concepts interactively — adjust parameters and watch the math come alive.

From the ancient elegance of the Golden Ratio to the modern power of Fourier analysis, each simulation turns abstract formulas into visual, intuitive experiences. Play with prime numbers, estimate pi using random points, or watch the Central Limit Theorem work its statistical magic.

8 interactive simulations

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Central Limit Theorem Demo

See the Central Limit Theorem in action: sample from any distribution and watch the distribution of means converge to a perfect bell curve.

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Fourier Series Visualizer

Decompose any waveform into sine and cosine harmonics. Watch rotating circles (epicycles) construct square waves, sawtooth waves, and more.

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Fractal Tree Generator

Grow recursive fractal trees by adjusting branch angles, depth, and length ratios. Explore self-similarity and fractal dimensions in botanical structures.

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Golden Ratio & Fibonacci Spiral

Explore the golden ratio through interactive Fibonacci spirals and golden rectangle subdivisions. Watch how the ratio of consecutive Fibonacci numbers converges to phi.

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Normal Distribution / Bell Curve

Visualize the Gaussian bell curve and explore the 68-95-99.7 rule. Adjust mean, standard deviation, and sample size to see how the distribution shapes data.

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Monte Carlo Pi Estimation

Estimate pi by throwing random darts at a square with an inscribed circle. Watch the approximation improve as more points accumulate.

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Sieve of Eratosthenes

Watch the ancient algorithm discover prime numbers in real time. Composite numbers are crossed off one by one as each new prime is found.

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2D Random Walk

Watch particles take random steps in two dimensions. Discover the square-root law of diffusion as walkers drift from the origin.