Drawing with Maths

Mathematical art simulations explore the aesthetic dimension of mathematics through interactive visual construction. Spirograph generators trace hypotrochoid and epitrochoid curves by coupling rotating circles of adjustable radius and offset, producing the infinite variety of Lissajous-like patterns familiar from the classic toy but derived from exact trigonometric equations. Tessellation builders tile the plane with polygons under the 17 wallpaper-symmetry groups, showing why only certain combinations of rotation and reflection can tile without gaps.

Hyperbolic-geometry visualisers render the Poincaré disk and upper-half-plane models where parallel lines diverge and triangle angles sum to less than 180°, making non-Euclidean geometry directly manipulable. Sacred-geometry constructors build Metatron's cube, the Flower of Life, and Platonic solids from compass-and-straightedge steps. These tools serve art students learning projection, mathematicians building geometric intuition, and designers seeking algorithmically generated pattern complexity.

Each simulation in this category is built with accuracy and interactivity in mind. The underlying mathematical models are the same ones used in academic research and professional engineering — just made accessible through a web browser. Changing parameters in real time and observing the results is one of the most effective ways to build intuition for complex scientific and engineering concepts.