Math Wonder Box List
Infinite Microcosm: Fractals and Recursion
11 DemosA visual marvel where infinite zooming reveals no end; freely explore a mysterious geometric realm reminiscent of an alien civilization.
Mandelbrot Set
Explore the mysterious Mandelbrot set, featuring infinite zoom and real-time rendering to experience the beauty of fractal mathematics.
Julia Set
Explore the stunning Julia set, observe infinite variations through real-time rendering, and discover the fascinating patterns of fractal mathematics.
Newton fractal
Explore Newton fractals and marvel at how mathematical ideas from over three centuries ago blossom today into a dazzling and intricate fractal world.
Dragon Curve
Explore the dragon curve and watch how a line transforms into a dragon through repeated folding.
Apollonian Gasket
Explore the Apollonian gasket: packing circles within circles, ad infinitum.
Hilbert Curve
Explore how a one-dimensional line can eventually 'fill' an entire two-dimensional space through continuous folding.
Koch Snowflake
How does the simplest snowflake evolve into one of infinite complexity simply by repeatedly adding a small triangle to its edges?
Lévy C Curve
How does a straight line grow into a complex fractal world?
Sierpinski Triangle
Explore how a single triangle transforms into an infinite world of triangles
Sierpinski Carpet
A mathematical carpet that is continuously hollowed out
Penrose Tiling
Give me just two types of tiles, and I can tile the entire plane; yet no matter how they are arranged, a truly repeating periodic pattern will never emerge.
Rhythms of Life: Natural Forms
5 DemosFrom a single leaf to a towering tree, witness how simple rules drive continuous growth, ultimately creating the lifelike forms found in nature.
Barnsley Fern
Explore the fascinating Barnsley Fern and see how simple rules can generate a lifelike fractal plant.
Fibonacci Phyllotaxis
Explore Fibonacci phyllotaxis and discover how simple patterns create the elegant, harmonious spiral beauty found in nature.
Pythagoras Tree
Explore the Pythagoras tree and experience how simple recursive rules grow into elegant, complex fractal trees.
Fibonacci Tree
Explore Fibonacci trees and experience how numerical patterns give rise to elegant, complex fractal trees.
Fibonacci Golden Spiral
Explore the Fibonacci golden spiral and see how numerical patterns transform into an elegant spiral.
Dancers of Space-Time: Dynamical Systems & Chaos
9 DemosFine-tune parameters with a touch of your finger and watch particles and trajectories dance to mathematical rules, morphing into butterflies, flowers, and nebulae; experience the fascinating journey of dynamical systems evolving from order to complexity.
Lorenz attractor
From weather forecasting to the "butterfly effect," explore how the Lorenz attractor uses simple rules to create complex and unpredictable motion.
Aizawa attractor
Explore the Aizawa attractor and observe how the trajectory of a point in three-dimensional space forms a mathematical structure of lifelike elegance.
Clifford attractor
Explore the Clifford attractor; by making subtle adjustments to a few parameters, watch as mathematical rules conjure up an endless array of blossoms, butterflies, and nebulae.
De Jong attractor
Explore the De Jong attractor and create complex, cloud-like patterns using simple rules.
Ikeda attractor
Explore the Ikeda attractor, repeating rotations and twists to create mathematical vortices of curling layers.
Gumowski-Mira attractor
Explore the Gumowski-Mira attractor and observe how, as parameters shift, the system transitions from regular periodic motion into complex or even chaotic states, while simultaneously generating patterns that strikingly resemble natural life forms.
Hopalong Attractor
Explore the Hopalong attractor and discover stunning worlds amidst a vast, chaotic parameter space.
Bifurcation diagram
Explore the bifurcation diagram and observe how a simple system transitions from stability and splitting, step by step, into chaos.
Noise Flow Field
Explore a noise flow field and watch a multitude of particles move together, driven by the wind.
Precision Mechanics: Geometric & Symmetrical Patterns
5 DemosRelive the pure joy of childhood Spirograph toys! Use rotation, periodicity, and geometric principles to instantly create deeply satisfying, symmetrical geometric patterns.
Lissajous curve
Vary the rhythm of motion in two directions and watch how a simple point traces an endless variety of Lissajous curves.
Epicycloid
Explore epicycloids and epitrochoids, and see how a circle rolling along the outside of another circle traces out complex and elegant mathematical curves.
Spirograph
Explore the mathematical world of the Spirograph, where rotating gears trace exquisite, symmetrical patterns through circular motion.
Rose curve
Explore the mathematical beauty of rose curves and create a myriad of petal patterns using simple rules of rotation.
Maurer Rose
By changing the method of selecting points, a simple mathematical rose is transformed into a complex and exquisite geometric pattern.
