Ancient Web: Junpei Sekino Turned Equations Into Fractal Landscapes

Part of the Ancient Web Collection.

A mathematical image can look like a mountain range, a decorated vase, or a strange creature. Junpei Sekino's website wants to show both the finished picture and the equations responsible for making it.

Visit Sekino's Fractal Art Gallery.

The page identifies Sekino as its author and carries copyright dates beginning in 1997. It has continued to evolve, with an update recorded in April 2025. Rather than discard older material when adding new work, Sekino organizes a long illustrated explanation called Stories about Fractal Art, plus separate two- and three-dimensional galleries.

Julia sets with a name and a formula

The 2D gallery gives individual images names such as Cloisonné Lion, Jady Lion, and Ruby Lion. The entries go beyond aesthetic descriptions to list parameters for the Julia sets and explain how tiny numerical changes can yield very different patterns.

Sekino connects those examples to the Mandelbrot set, which can be used as a kind of map to find Julia sets with different properties. Some are connected in one piece; others consist of disconnected points. The visual difference is not always apparent at a glance, and the gallery calls attention to that difficulty.

The 3D gallery is more playful. A mathematical height function becomes a mountain, while mapped fractals decorate a globe, vase, bowl, or broken drum. Works named Birdless Island, Tamarack Forest, Mandelbrot Moon, and Newton Apple show how one idea can escape the flat graph.

A classroom that refuses to separate art and math

The main text covers orbits, dynamical systems, the logistic equation, Mandelbrot and Julia sets, Newton fractals, and coloring algorithms. It also discusses Hokusai's Great Wave, making a comparison between historic printmaking and computer-generated form.

Some of the site reads like a specialized textbook; some like a gallery guide written by an enthusiastic artist. Those two sides support each other. A visitor intrigued by the artwork can find the mechanism, while a reader learning the mathematics can see why anyone would care about a particular iterative function.

Sekino has kept a visibly older page style while extending the collection over decades. That is a stronger historical claim than mere nostalgia: it is a continuing record of creative mathematical experimentation.

Browse the original fractal gallery and its three-dimensional landscape collection.

Part of the Ancient Web Collection.