Julia set
FeaturedIterating z to z squared plus c on the complex plane draws a fractal boundary and its self-similar structure.
羊·實驗
Experiments in mathematics and algorithms
In-depth works
Works
Each one focuses on a single mathematical object: the formula, an interactive figure with adjustable parameters, and a full visual explanation.
Browse works → InteractiveExplore
Start from one big idea and follow several interactive experiments and what to notice in each.
Browse topics →Featured
Curated picks, chosen for visual impact and a complete interactive figure.
Spirograph curve
FeaturedA hypotrochoid is the path of a pen on a circle rolling inside a fixed circle; R and r set the corners, and d sets how sharp they are.
Complex numbers and Euler's formula
FeaturedOne rotation, read as complex multiplication, a point on the unit circle, and the cosine and sine of the same angle.
Latest works
Tangent and a secant
From a point outside a circle, the square of the tangent segment equals the secant's external part times the whole secant.
Two secants
From one point outside a circle, each secant's external part times the whole secant is the same number.
A triangle on the disk
On the unit disk, an equilateral triangle whose sides are arcs orthogonal to the boundary has a smaller angle sum nearer the edge.
Latest topics
Enter a mathematical idea by topic and build its core picture with interactive visualizations.
Secants and tangents
At one exterior point, the secant product and the square of the tangent segment are the same number.
Open topic →Powers and roots
The same addition of arguments shows up in a product, in an nth power, and in n equal roots.
Open topic →Iteration dynamics: from convergence to fractals
Apply one rule again and again, and compare fixed points, short periods, dense long-run values, and self-repeating fractals.
Open topic →