*archive // 2005.05.23 01:08:24 [her]*

**Mit Johan Gielis, Erfinder der "Super Formula" (einer universalen geometrischen Formel für die Repräsentation elementarer bzw. natürlicher Formen), Autor des Buchs "Inventing the Circle" und Gründer der belgischen Software-Firma Genicap, sprach Eckehart Röscheisen über die Hintergründe seines "Supergraphx Shape Explorerers" (wir stellten das Illustrator und Photoshop Tool bereits vor), über die Entwicklung der Mathematik, die Creative Tools der Zukunft und über Sinn und Unsinn der Patentierung von Technologien. Das englischsprachige Interview gibt einige interessante Einblicke.**

**Screen2.0:** "Supergraphx" is the most unusual plug-in I encountered because it is basic and complex at the same time which might boost productivity of graphics designers who are dealing with natural forms creation. Where did you get the idea for the mathematical foundation (also called the "Gielis Superformula") and this interesting piece of software?

**Johan Gielis:** Initially we developed software to make graphics much more simple. You can find some examples of our 3D modeller, which encodes the full geometry in a precise CAD CAM way, in extremely small file sizes. An example is found at: users.skynet.be/bert.beirinckx/3D%20Examples%20Modeler.htm.

The airplane and any of the shapes below are encoded in less than 600 bytes. Can you imagine? This is less than the file size of the short cut pointing from your desktop to any file on you computer. Only the racecar, consisting of about 20 object is 900 bytes. Again, no triangles, no tricks, no libraries; pure geometry, all point on the shape and inside are uniquely encoded.

Also bear in mind that apart from the natural shapes, also abstract shapes such as circle, ellipse, regular polygons and in 3D spheres, cubes, and any of the shapes you can make, are encoded with the same formula. So it is certainly not only about natural shapes, it is about Universal Shapes.

So we had technology, and we needed to convert it into products. Graphical artists like Albert Kiefer and Tom Krikken, convinced us that while small file sizes and so on are great, the real value for them was in generating shapes, sampling in a mathematical universe of shapes which no one had ever seen before. That is how Supergraphx was born. Supergraphx wants to be a first step towards a creative machine. Now computer are just stupid computing machines. But what if we could make this machine into an extension of the hunman creativity? In this case shapes, but could be much more.

So we programmed the computer to have a seamless integration into existing software, with slider bars for Adobe users, since they do so all the time.

**Screen2.0:** What do you think makes "Supergraphx" so unique?

**Gielis:** Supergraphx is about Creation, Variation and Storage. The variation gives new suggestions in milliseconds.

Also local control is possible. We also realized that the vectors in Adobe software are already very powerful, so we decided to keep the surprise element as main feature, not the control element (although "cpoints" refer to both creativity and control). There are already a number of simple applets and so on out on the internet, but we keep developing to turn it into something powerful.

That we are on the right track is proven by the many positive quotes we get. The latest one is in Computer Arts: "It's the kind of plugin no self-respecting designer should be without".

It is our aim to show that such software should be standard in any design program. Let the computer help you in thinking up new shapes and designs. Optimize that workflow, too.

**Screen2.0:** "Supergraphx" involves a lot of math stuff. What is it that makes this software so special in your eyes? Could you explain it for non-mathematicians what's the special thing of the "Gielis Superformula"?

**Gielis:** It involves just a little bit of math stuff.

This is described in my book "Inventing the Circle". It all started with Piet Heins "Superellipses", which date back to 1818 (Gabriel Lamé). When I read about these shapes (and that squares and circles are not that very different) I realized that if I had been told in high school that these shapes could simply morph into each other like inflating a balloon in a box, maths would have been much more interesting (in fact I disliked maths in high school). Instead, we are taught from our early childhood, how different all these things are, with hardly anything in common.

Secondly, I realized that I had seen these shapes in bamboo and other plants, and realized that the optimization principles were similar to the use of superellipses in architecture and design by Piet Hein.

But I still was stuck then with the limitation to four symmetry of squares. The superformula effectively is an elegant solution to this problem. In fact, it is as simple and at the same time more general than Pythagoras' theorem itself (which like the circle and square, is a special case of the SF).

Last year I came into contact with Prof. Verstraelen (Geometry, University of Louvain) and he could formally state what I had conjectured. That the shape of flowers and black holes is very much the same. In "Annexe" you will find an article by him (very difficult), showing that what dwells in the world (we, flowers, shells, DNA, ...) and the world in which we dwell (space and time itself) is described by a single formula.

So, pretty exciting stuff all that.

**Screen2.0:** Why did it take so long to discover the Superformula?

**Gielis:** Actually, that still surprises me. This formula could have been the basis of geometry thousands of years ago. Perhaps it was. It could have been discovered again during the Renaissance, when analytical geometry was founded. It was not. To me, the Superformula is proof that in science, certain paths are followed while other, equally interesting paths, slip by undiscovered or are simply forgotten. For more than 2000 years, math and science have focussed on Euclidean geometry with fixed rulers. This seemed the most natural and straightforward way to describe our world. But the Superformula proves that another approach is much more powerful.

**Screen2.0:** Why did you choose to start private company?

**Gielis:** I like to do things my own way. Experts always give you 10 reasons why something won't work. The Superformula works, and I believe it will have a tremendous impact in science, education, and technology. In each of these fields there is a considerable amount of inertia. With my own companies I can develop my own ideas.

I started out my own company to develop my ideas further in education, science and technology. This is also the order of fields where my ideas would encounter most inertia for acceptance.

We chose for technology (Genicap Corporation) because acceptance would be more rapid and to generate some revenue in order to finance further investigations and research.

Keep in mind that the superformula basically is very simple, hardly more complex that the equation of the circle.

**Screen2.0:** You applied the theory behind your "Gielis Superformula" to vector drawing (Illustrator plug-in), pixels (Photoshop plug-in) and 3-D modeling ("3D Shape Explorer", Cinema4D plug-in). Have you further ideas where this simplified modeling of forms and condesed representation of graphical data using these math foundations might make a lot of sense, too?

**Gielis:** Lots of ideas, from cosmology to DNA and pharmaceutics. Mind that the formula is a relation between numbers, a simple one, and that the graphical representations can be of many different forms, including sounds and other signals. So we are just at the very beginning.

**Screen2.0:** Do you have further plans for products? What can be expected next from Genicap?

**Gielis:** We intend to remain a small company, focusing on intellectual property and generating interesting ideas.

**Screen2.0:** Do you also talk to companies like Adobe?

**Gielis:** Taking it to the big companies means pushing and keep on pushing. Even if you have a formula that is so powerful, it does take time to convince people, that it can do things better, faster ... in all upgrades of software, people are given the idea that it is the ultimate but what we have now differs very much from what was software 10 years ago. To convince big companies, takes finding the right entries and so on. Not easy for a small company. But we will succeed.

**Screen2.0:** You are researcher and the mastermind behind Genicap and also book author of "Inventing the Circle". What is your background and how do you make money today?

**Gielis:** Money is only a motivation for me insofar that it can help me fund further research. I will go back to research in the near future, once Genicap is on the rails.

**Screen2.0:** You talked about possible applications of the formula in other areas. How might the formula be applied to sound?

**Gielis:** I have an Excel file you can experiment with. It shows, apart from the polar views also 'sound' like views (this could be implemented as frame and lines too in Adobe Illustrator). It basically is a simple program to generate shapes and waves. Such shapes can be used for sound synthesis. We have tried and it generates some weird sounds, i.e. square or triangular sounds instead of AM or FM.

**Screen2.0:** In which area do you see the biggest chance for innovations in the near future looking at the development in graphics software and algorithms today?

**Gielis:** Currently mainly in generating shapes, but in 3D it has the advantages of implicit objects and surface objects combined. Think raytracing, point evaluation, easy constructive solid geometry. But for the time being, I think we want to stick mainly to graphic artists, since this gives us the right exposure. Building in specific constraints is the next step (for example: all variations should fit inside a box of that size, whereas all variations are pretty wild now). However, sampling in the whole math space is more interesting at present. Just think how easy it would be for a perfume bottle designer to have all variations as solution to his specific demands.

**Screen2.0:** Your software is patented. Why?

**Gielis:** The use of the formula in a computer in a broad sense is patented. It is freely available for research, but commercialization of products will fall under the patent. But that then is a question of business opportunities and cooperation between companies. A good example is Bezier curves: as far as I know, the handles have been patented by Adobe. Without this, the vectors would be largely uncontrollable.

Patenting is a strange, yet challenging subject. Essentially, since already in the very early stages of my discovery, i realized how powerful it was (if e = mc2 is a special case too ...), so iniitally the patenting was done (how strange it may seem) as a compromise. I did not want to reveal the formula at all (given that all good discoveries are destined to lead to bad/evil applications). But Prof. Gerats of Radboud University of Nijmegen convinced me to do that anyway. So the patent was a compromise to be at least able to some extent to control whatever is made with it, even if ten years from now.

**Screen2.0:** What do you think about these standards vs. patents discussions which are often led when comparing Europe to the United States?

**Gielis:** It is an interesting fact that the patent has been granted in Europe first before the US.

Whatever one says, patents and intellectual property in general, are driving forces for innovation. That is at least the basis. Sometimes this leads to excesses, but all in all, patenting can be used in many ways. All in all, a patent is one of the means or tools in a business. Sometimes an important one, sometimes not. All depends.

Consider this one: I had published the formula and a major company had read about it and patented its use in a computer. Then we would be in trouble. Because then I would have had to pay for using my own invention.