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.

# art

# 090

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 18^{th} 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.

# 021

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

45*((a*(51+sqrt(55))/1)^5*x^12-1*y^2)*((a*(1+sqrt(5))/2)^2*y^2-1*z^2)*((a*(1+sqrt(5))/2)^2*z^2-1*x^2)-1*(1+2*(a*(1+sqrt(5))/2))*(x^2+y^2+z^2-1*1)^2

# 011

# 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