knot picture knot picture

Ken Brakke
Professor Emeritus
Department of Mathematics
and Computer Science
Susquehanna University

Phone: 570-495-0452 (mobile)
Snail mail: 2603 Pacific Highlands Ave, Ferndale, WA 98248

catenoid example tombstone example

The Surface Evolver

Version 2.70, August 25, 2013

My Surface Evolver is an interactive program for the modelling of liquid surfaces shaped by various forces and constraints. The program is available free of charge.

book cover

Book on Microdroplets, using Surface Evolver

Jean Berthier and I have collaborated on a book about the behavior of liquids in microfluidic circumstances. Over a hundred Evolver models, available for download from the book's website (if you buy the book).

book cover

Book on Open Microfluidics, using Surface Evolver

Jean Berthier and I have done another book, about liquids flowing in channels that are not completely enclosed. Includes lots Evolver models, available for download from the book's website (if you buy the book).

Joseph Plateau

Plateau's book translated into English

The result of my amateur attempt to translate Joseph Plateau's famous 1873 book on soap films and surface tension.


Random Fractals

A gallery of random fractal images generated with iterated function systems (IFS), along with my own applet to generate more. Infinite complexity and amazing variety from simple rules!

knot space gate


A program for visualizing multiple universes connected by gateways formed by cosmic strings. The image shows five universes (with different color skies) connected by a string in the shape of a trefoil knot. Polycut reveals how soap films are least-area boundaries between universes.

Kelvin tetrakaidecahedra

Beating Kelvin's partition of space.

What is the least area way to partition space into unit volumes?

wet X

The wet X.

A Java applet showing the equilibrium states of a 1-dimensional soap film spanning the corners of a rectangle with liquid in the interior of the film.

wet X

The Double Bubble Pipe.

A Java applet showing the stable equilibrium states of a multiple-bubble pipe. Illustrates how joining stable systems can result in an unstable system.

periodic surface

Triply periodic minimal surfaces

Surfaces of zero mean curvature that repeat periodically in three dimensions.

cube soap film

Soap film cones

Which soap films on wire frames form perfect cones straight to the center? There are surprisingly few.

film on trefoil

Soap films on knots

Knotted wires make for some very interesting soapfilms!

film on Borromean Rings

Soap films on the Borromean Rings

The Borromean Rings are three rings linked so that any pair of rings are not linked, but all three are (i.e. cannot be pulled apart). The Rings support many soap films. Go here for static images. For 3D mouse-spinnable images, go here. And for better 3D mouse-spinnable images using the upcoming WebGL 3D technology, go here. (Only works on FireFox 4 Beta or later, suitably configured. Before loading, browse "about:config" and set "webgl.enabled_for_all_sites" to "true"; this setting will be permanently remembered.)

opaque cube

The Opaque Cube Problem

What is the least area surface that can block any ray of light from passing through the interior of a cube?

space alien

Statistics of Space Aliens

Even if the galaxy potentially has millions of space-faring civilizations, the first such civilization probably gets about a 100 million year head start on the second. We look to be the first, so the galaxy is ours to colonize without opposition!

a pageMy papers.

100 grainsGrain growth movie.

A Surface Evolver simulation of 2D grain growth, starting with 100 grains. The starting configuration is the Voronoi diagram of 100 random points. Periodic boundary conditions. 1.6MB mpeg. Also 1000 grain movie (8 MB mpeg) and 10000 grain movie (10 MB mpeg).

a pageRuler and compass constructions.

These are mainly for the benefit of my Geometry class. There are step-by-step constructions for 29 basic constructions, plus some more challenging ones.

Math Senior Colloquium

A page of suggested topics for our Mathematics Senior Colloquium.

Mathematics Department home page
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