mathematics

Mathematical Art

Where mathematics meets beauty — Penrose tilings, spirograph curves, phyllotaxis spirals, and the mesmerizing patterns of reaction-diffusion systems.

mathematical artgenerative artPenrose tilingspirographphyllotaxisL-systemsreaction-diffusion

Mathematics is not just useful — it is beautiful. The same equations that describe physical laws also generate stunning visual patterns. From the aperiodic perfection of Penrose tilings to the organic forms of reaction-diffusion systems, mathematical art reveals a deep aesthetic hidden in abstract structures.

These simulations generate visual art from pure mathematics. Create spirograph curves by adjusting gear ratios, grow sunflower-like phyllotaxis spirals using the golden angle, explore the infinite variety of Lissajous figures, and watch reaction-diffusion equations paint organic patterns in real time.

5 interactive simulations

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L-System Fractal Plants

Grow fractal trees, ferns, bushes, and flowers using Lindenmayer systems — simple rewriting rules that produce stunningly realistic plant structures

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Lissajous Figures

Draw beautiful Lissajous curves from two perpendicular oscillations — explore frequency ratios, phase shifts, and the figures used to calibrate oscilloscopes

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Phyllotaxis / Sunflower Spiral

Explore how the golden angle creates the optimal seed packing found in sunflowers, pinecones, and pineapples — and watch Fibonacci spirals emerge from pure mathematics

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Reaction-Diffusion Patterns (Gray-Scott)

Watch organic patterns emerge from chemical equations — spots, stripes, spirals, and chaos generated by the Gray-Scott reaction-diffusion model that explains animal coat patterns

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Spirograph / Hypotrochoid Curves

Generate mesmerizing spirograph curves by rolling one circle inside another — explore the geometry of hypotrochoid and epicycloid curves through interactive animation