Update 10, 2016

I was preparing some artwork  (The 12-30 project, #211 – July 30 ) for an upcoming exhibit and I clicked the emboss filter – almost by accident. And here it popped up – a next to perfect representation of a (topological) 4D perspective of a Klein bottle – from the outside looking in. Thanks @Mathematica, and thanks #Richard Bennigan for the original script.




March 31 – 090

KnotPlot. Satellite knot.

In mathematics, a knot is an embedding of a circle in 3-dimensional Euclidean space. Knots have been part of our scientific and cultural exploration of the world since prehistorical times – in China as well as in the Celtic world. The first mathematical theory of knots dates back to the 18th century. Today knot theory extends from the study of DNA to quantum computing.

KnotPlot is an OpenGL program that has a database of more than 3,000 knots. After scripting in ContextFree all of March, I will explore this new graphic environment for the entire month of April.



Jan 21 -021. Surfer – Barth Sextic #1

Moving to the third series of images extracted from the Surfer program.The Barth sextic is a surface of degree 6 (sextic). It was defined by mathematician Wolf Barth in 1966 and is composed of 65 singularities.

A 1.00 zoom 0.45


The 12-30 project – Foreword

After the 1 image a day for 364 days, I am changing the format of my ongoing exploration of the digital world.

This year’s project – 1 program a month – 30/31 images per month within that program. The challenge will be – Can I get a self standing original visualization with a minimum of alteration/intervention? Indeed, one hour a day maximum is the framework I will attempt to keep. We’ll see how far it goes…..

Apps I’ll be using: Surfer, 3DMathXplor, ContactFree art, Autodesk-Maya, Rhinoceros, SeamlessMaker, Tessellation, KnotPlot, Adobe-Premiere, Adobe-After Effect, Adobe-Photoshop, Corel-Paint. – And/maybe other I don’t yet know of….

And because the mathematical formulae I’ll use belong to all of us – I’ll post the programs’ references & equations – in case some are interested to explore the software on their own.

Jean Constant, 01-01, 2015