INTERVIEW: FRANCESCO DE COMITÉ MAKES math VISUALLY remarkable

Francesco de Comité is an Associate professor in computer Science at the university of Sciences in Lille, France, where he researches the 2D as well as 3D representation of mathematical ideas as well as objects. He’s provided papers on a range of topics including anamorphoses, experiments in circle packing, as well as Dupin cyclides. His present job includes modeling as well as 3D printing sea shells. He’ll be providing a paper on the topic at Bridges Conference in July. You can find his jobs on Flickr as well as on Shapeways.

Hackaday: one of your recent jobs includes producing fractal patterns as well as warping them into biologically-correct sea shell shapes, which you then print.

FdC: Modeling seashell shapes is an old topic–Moseley, 1838, D’Arcy Thompson beginning of 20th century. A seashell can be defined as a curve turning around an axis, while equating in the direction of this axis (i.e. on a helicoidal trajectory), as well as growing in size at the exact same time. This was modeled for computers in the ’60s by David Raup.

Drawing patterns on seashells was explained by Hans Meinhardt using a design of chemical reactions (activator-inhibitor), in the exact same spirit as Turing’s work on morphogenesis. integrating these two works, as well as utilizing 3D printers instead of 2D renderers, we can develop realistic seashells, either by copying existing shells, or inventing new ones. A 3D design is not just a juxtaposition of a significant number of 2D views: manipulating 3D designs can assist you comprehend the object, discover details, as well as so on.

I was curious to see if making a 3D seashell was possible. Moreover, I show that this can be done with simple tools — well, except the 3D printer.

Can you tell us a bit about the software and hardware involved?

All the process is done utilizing Blender, as well as the programs are written in Python utilizing Blender’s script facility. The 3D printer is a ZCorp ProJet 460, which utilizes a powder similar to sand, as well as which can output colored objects.

You mentioned D’Arcy Thompson’s work at the turn of the 20th century, in addition to Meinhardt more just recently — was it actually a situation of all of the math having been done for you already?

I have some math background, however I am more a programmer/computer scientist than a math scientist. In general, for all my works, I utilize maths already written by other people. when I have coded an equation, a math concept, I can play as well as tune its parameters, as well as see what happens. We might phone call this ‘experimental maths’.

What was the biggest surprise or revelation you encountered while designing the shells?

3D printing is not an precise science. I made some misses, however it enables me to cut a 3D printed shell in half, as well as see exactly how it was printed inside. Not precisely as I believed it would be. It provided me a much better comprehending of what my program was doing.

I’m reading (okay, skimming) Meinhardt’s book “The Algorithmic beauty of Seashells” as well as I noticed the author included fundamental code for a seashell pattern simulator. Was that old code an example of the kind of research study you had to equate into more “modern” formats?

This was a funny part of the project. In the 1990’s, the book was offered with a 3 1/2 floppy disk containing programs written in BASIC. The visitor was able to produce the patterns explained in the book, as well as test them with other parameters. recent versions of the book don’t contain this disk anymore.

Then I discovered that a library in a university in Montpellier, France still had the disk. I contacted them, they discovered a floppy disk reader, installed it on a computer, as well as sent me a backup of the disk. This was the very first part. I was not able to discover a fundamental interpreter to run the programs, so I decided to checked out the programs as well as equate them, very first in Java/ImageJ to test the patterns, then in Python, to integrate them in the python script utilized in Blender to produce seashells.

It is disturbing to see that programs written less than 20 years back are already difficult to use.

With regards to your work — not necessarily to nature in general — do the fractal patterns on the surface of the shell have a connection to the curvature of the shell?

There is no link between the patterns as well as the shape of the shell. it appears like those are two independent processes — however I am not a biologist! In fact, you have a number of possibilities for putting a pattern on a shell: mapping an picture on it (you think about the shell as a 2D twisted screen) This distorts the picture strongly. right here is Mona Lisa (image to the right).

A great deal of your jobs seem to include taking something digital as well as making a physical version. I can comprehend utilizing a digitallymanaged machine like a 3D printer, however you likewise do a great deal of jobs with cut paper, cardboard, as well as wire. What type of difficulties do you encounter equating your digital styles into such imperfect media?

Initially, my goal was to make mathematical ideas (curves, equations..) tangible/visible. I began with 2D images, then 3D printed objects. trying to equate these ideas with other means came naturally. The final goal would be to develop objects without utilizing computers at all.

But I still requirement computers: I commonly produce online versions of the objects before to develop them in genuine world. You are right, I have to go from a perfect world to the genuine one. however I don’t believe this late one is imperfect; in truth the versatility of genuine material is of excellent help, for building polyhedra with playing cards for example.

The difficulty is more at the beginning of the process: exactly how to utilize math to compute the right info I will requirement to develop the object.

You’ve developed a significant assortment of polyhedra out of paper. What’s the most challenging polyhedra you developed that way, exactly how did you style as well as develop it, as well as exactly how long did it take?

I am indebted to Magnus Wenninger for this part of my work. I am utilizing his book “Polyhedron Models” in which he details designs for building a great deal of polyhedra; I just complied with his instructions. building a design takes 2 or 3 weeks (working in the evening only). the most challenging I tried to make was the 14th stellation of the icosahedron, however there are still a great deal of designs in the book I didn’t build.

One of your jobs includes building digital designs of Catalan solids utilizing playing cards. What about utilizing cards interested you as compared with (for instance) origami paper? Did you develop any type of of the Catalan solids in genuine life?

The difficulty is different : I produce online designs (using Povray), diverse the area between the cards, their angle, etc… When I like the model, I compute the cuts to be performed in the cards, as well as develop a template. The second part of the task is then to assemble the cards. I referred to George Hart’s work on Slide-Togethers.

The work is extremely different from origami. I am not able to invent origami designs (just comply with instructions).
Playing cards are a great material, they are at the exact same time stiff as well as flexible. Their glossy surface makes it simple to slide them one inside another.

My preferred of your jobs is your Dupin cyclide series. I like exactly how you deal with the torus utilizing so many materials, with woven paper, cardboard, as well as cable versions. What about the cyclide interests you?

Cyclides can be designed utilizing only circles. It is a non-trivial item defined by the most trivial closed curve. These circles can be cardboard disks, 3D printed rings… working for a number of years now on cyclides, I have a collections of functions as well as programs I can manipulate like tools to design new representations.

And when I satisfy some problem, I can go back to the torus, solve the issue there (it is commonly easier), as well as then transform it back to compute the solution on the cyclid. I believe likewise that cyclid are attractive for other people, they are appealing since they seem simple at very first sight, then one realizes  that they are not.

Do you have any type of concerns for [Francesco]? Leave them in comments.