Art from code - Generator.x
Generator.x is a conference and exhibition examining the current role of software and generative strategies in art and design. [Read more...]
Tag: math

This page shows all the posts tagged with . Other popular tags are: , , , , , , , , , . You can also browse all tags together.

David Dessens: *#07 video

David Dessens: *#07 video

David Dessens (see previous entry) has posted a new video called *#07 using his trademark combination of GPU shaders and mathematical formulas. As usual he manages to imbue his synthetic structures with warm organic qualities, using color and irregular forms to great effect. See also this blog post for more images.

The video is for an as-yet unnamed HD video project, and is rendered in non-realtime using VVVV. Dessens has also been experimenting with creating high resolution images for print use. It will be interesting to see how he develops this work.


Eric Gjerde of Origami Tessellations recently Flickr'ed some wonderful images of Ron Resch, computer graphics pioneer, mathematician and origami innovator. His credits include patents for “self-supporting structural units” using tessellation techniques, as well as “geometric designs” (structures for spaceships) for Star Trek: The Motion Picture (1979).

Of the many pioneering projects Resch was involved in, the 1974 Vegreville Pysanka is one of the most spectacular. A pysanka is a Ukrainian Easter Egg, decorated with intricate patterns that are often geometrical in nature. Using computer graphics techniques that were then cutting edge, Resch designed and built a giant pysanka sculpture using tiling techniques to create both structural integrity and geometric visuals. The photo shown above top left shows the sculpture being dedicated by Queen Elisabeth II.

Known also under the moniker “World’s Largest Easter Egg”, the Vegreville Pysanka is a wonder of mathematics. It is also considered the first-ever physical structure to be constructed entirely based on computer-aided geometry. Resch built it using principles he had pioneered in paper-folding experiments, techniques he also intended to be used for constructing larger structures. Buckminster Fuller’s geodesic domes are probably better known, but Resch’s ideas of folding structures open the door for more geometric wonders.

Be sure to read Eric Gjerde’s post about Ron Resch over on Origami Tessellations. Pictures from Ron Resch home page and Flickr.


Nicholas Rougeux: MengermaniaLevel 3 / Level 4 at 0.25%

Nicholas Rougeux likes Menger sponges. You know, the classic fractal shape created by Karl Menger, the one that gains an infinitely large surface area as it is iterated. The sponge has long been a favorite with computer graphics enthusiasts, but Rougeux does them one better. He builds Menger sponges as Origami sculptures using index cards.

Back in 2003 Rougeux built a level 3 sponge with over 66 thousand units (see image), taking over 7 months. This time he plans to build a level 4 version, a substantially more ambitious project that will entail 1.2 million units. So far he is at 0.29%, with 3774 units built. You can follow his progress and see more images over at Mengermania.

The Mengermania site also has a handy About section, giving more details about the sponge, as well as instructions about how to build one yourself. Definitely a way of impressing your friends. After all, the final result is very attractive.

David Dessens: Sanch TV

David Dessens (aka Sanch): Linear / Math surface destrukt

David Dessens’ work with VVVV has been generating a lot of interest since the first appearance of his shell-like objects on the VVVV pages. With the launch of his own blog Sanch TV he displays a range of hugely impressive formal experiments, bursting with voluptuous curves and saturated color. It is proof not only of Dessens’ personal talent, but also of VVVV’s qualities as a production tool.

Most of his experiments involve the use of vertex shaders, filters that affect geometry but which are executed directly by the graphics card (GPU) rather than the computer’s internal processor (CPU). The GPU is a specialized chip dedicated purely to graphics operations, and farming out computation to it results in lightning-fast execution. Some of Dessens’ experiments are based on shader implementations of mathematical "supershape" surfaces. These meshes are then distorted and manipulated further. But even working with standard mathematical formulas as raw material, Dessens manages to produce images with a unique visual style.

At the moment Dessens’ interests lie mostly in live visuals, but it will be interesting to see how his work develops. He is currently artist-in-residence at VVVV developers Meso, which should be a guarantee of more interesting work from him in the near future.

Be sure to see Dessens’ showreel, generated purely in realtime. As an extra bonus for wannabe VVVV hackers, he also posts shaders and patches on his blog.


Just came across Krome Barratt’s wonderful Logic & Design in Art, Science and Mathematics. The book outlines ideas somewhere between art, design and science, applying semi-scientific evaluations to aesthetic issues. The quote above jumped out:

…We enjoy winding paths packed with friendly variety and affording appetising glimpses of future delights with their assurance of survival into the middle and far distance.

Now, if only life was that easy.

Falstad: 2D Vector field

Paul Falstad: 2D Vector field

Falstad: 3D Waves simulation

Paul Falstad: 3D Waves simulation

Workshops on computational design and generative art tend to start with a sense of excitement. The participants find themselves exhilarated as they discover that forms can be made to move and interact with just a few lines of code. But then a certain point is reached, where the words “trigonometry” and “vector” are mentioned. And often exhilaration turns to despair.

Regardless of whether you believe the old “right brain / left brain” clichee that creative people are bad at math and vice versa, there is a wall of knowledge that divides the scientist from the creatives. The old mistake is to think that the scientists have all the knowledge on their side, since they can to refer to physical laws and all kinds of theorems. The artists and designers are left with “soft” theories of communication and art history, much maligned by the rational scientific community. But put a physicist in charge of an advertising campaign, and you will most likely get a spectacular failure. In fact, it will be much like a nuclear reactor built by cubist painters.

Yet aesthetics is a field of knowledge, with massive amounts of empirical data to back it up. Advertising execs and industrial designers can refer to demographic studies, ergonomic principles and historical and cultural biases as to which color best expresses joy. But the artist is sometimes left with no option but to say “it is so”, without the faintest data to back her up. Still, no creative would doubt that any artist’s method is based on a mass of internalized knowledge. It’s just a shame it’s so hard to communicate.

A simple “you know stuff, too” pep-talk will never get creatives over the mathematics threshold. Some will give up, some will find unexpected resources within themselves and yet others will learn to build on work done by others. That’s where people like Paul Falstad come in handy.

Falstad has published a rich resource of Java applets demonstrating physical and mathematical principles, many of them with source code included. One can find wave simulations, vector fields, digital signal filters, magnetostatic fields and even quantum theory. And while this is still heady stuff, at least it’s in a visual form.

Another famous source is Paul Bourke. He has published papers, algorithmic how-to's and even information on common file formats. Many computational designers acknowledge a deep debt to Bourke’s work.

Want to model organic or mechanical motion? Go pay Craig Reynolds a visit, he created the classic Boids algorithm and has plenty of data and code online. This is essential reading for learning how to describe movement in terms of intention and action, rather than just as a set of changing X,Y coordinates.

The moral? There is hope. Any student who learns to google creatively will find help for even the most obscure problem.

(Via Andreas Nordenstam on BEK’s BB list.)

Osinga & Krauskopf: Lorenz crochet

Osinga & Krauskopf: Lorenz crochet

Needlework is in the air: Paul commented on the Freddie Robins post about crocheting in the hyperbolic plane, then today has a post about stitched DOS commands.

The infosthetics post also reminded me of a project by Doctors Hinke Osinga and Bernd Krauskopf, both Ph.D.s in Mathematics, who created a crochet model of the Lorenz manifold. (Yes, those are real crochet details you see in the picture.)

The Lorenz attractor is one of the best known strange attractors, but this has to be the most labor-intensive visualization of it ever produced. Some googling unearthed their scientifc paper on the project: Crocheting the Lorenz manifold at the Bristol Centre for Applied Nonlinear Mathematics. Supposedly, the good doctors have promised a bottle of champagne to anyone who repeats their effort.


I’ve been perusing the work of Victor Ostromoukhov and came across this paper,
which he offers as a free download. It’s an overview of ways of describing tiling
patterns. There’s a lot of art yet to be pried from tiling.
1) Pretty pictures.
2) Technique overviews.
3) Sizable bibliography.

Full title: Mathematical Tools for Computer-Generated Ornamental Patterns