The Mandelbrot Bakery

Interview with Ingrid Daubechies

Which theorem or mathematical concept inspired you?

The whole idea of the Bakery started because I have been frustrated for many years by the fact that  interesting cookie shapes are very wasteful.

When you make cookies yourself, you roll out the dough, and you can of course cut it into diamonds or squares or rectangles, and for some cookies that is done. But most often, you’d have interesting shapes that you punch out with a cookie cutter, and then you have all this dough that doesn’t provide enough space to punch out more shapes, and you reassemble it, you roll it out again, and you punch out more cookies. And it’s wasteful of time, but that is not the  worst thing. Because the dough needs more flour for rolling it out, it absorbs more flour, and the cookies become less fine every time you re-roll the dough.

So I have thought for a long time that it would be nice to have cookie cutters that tile the plane, so that there would be no waste. Some years ago I designed such a cookie  shape for Pi Day (March 14); I made such cookies and I thought they were very cool.

When I mentioned this to the  other team members, they said “Oh yes, that would be great!” So we have a bakery, and that will  illustrate a tiling. And then people said “we could illustrate other things! We could  have a tiling on the floor, and we can have links with dynamical systems, and with symmetry groups. . . and that is where it all came from. 

How are these concepts illustrated in the Mandelbrot Bakery?

To illustrate all of these ideas in the Bakery, we have a baker, who is standing there, working, and he is in the process of rolling out his dough with cookie shapes that tile a plane. His table also has a very interesting shape: its side profile looks like a ‘U’ lying on its side, or a horseshoe. This alludes to a model in dynamical systems theory in which portions of space get stretched in one direction, and compressed in the perpendicular direction; they then get folded over to fit again in the same location as before. The whole operation is sometimes called the “baker’s transformation,” because it is similar to an operation you perform when making, for example, puff pastry dough.

On the floor we have a tiling by non-regular pentagons, created by Marjorie Rice, who was a housewife interested in mathematics: she designed tilings that had not been previously discovered. On one of the Bakery walls we have symmetry groups illustrated by a wallpaper showing all of the wallpaper groups that can be knitted – this will be a knitted wallpaper, by Susan Goldstine. There are 17 wallpaper groups: 8 of them cannot be knitted easily, because they have 30, 60 or 90 degree rotational symmetry, but 9 of them are knittable, and we’ll show them there.

What challenges did you face during creation?

Challenges in designing the bakery . . . There were many . . .

First: thinking of ideas –  well, that was not really a problem, the problem was integrating them in such a way that they all fit, and the Bakery doesn’t become too crowded. There are many, many different represented ideas, but many are in small details in the Bakery. Some participants thought that the Bakery would become too full. But as long as we make use of details that don’t overwhelm the space, there is room for all of that, I think. This will be a piece where even people who have seen it quite a few times, who walk by it all the time, will say, “Oh, look at that! I hadn’t seen that before. Now, that is really cool.” 

There is also the challenge of actually making it. The walls will be made out of wood, and some of that will be milled and cut very precisely by Edmund Harris, helped by Gavin Smith.  Gavin is not himself a member of the team, but he is one of the woodworkers we commissioned to  build the base of the whole structure, given that we could not have access to the woodworking group at Duke University, because of COVID. 

Who worked with you on the Mandelbrot Bakery?

Many people are working on the Bakery. Of course, in our discussions, everybody participated, so there are ideas that came from many people who aren’t members of the Bakery team.

I already mentioned Susan Goldstine, who came up with  the idea of the Marjorie Rice tiling on the floor, and who is knitting the wallpaper groups for that one special wall. I also mentioned Edmund Harriss; he is not only making the walls, but is also designing beautiful symmetric patterns that involve pentagons and heptagons in the side wall opposite the mouse wallpaper. The patterns involve both pentagons and heptagons, because this wall marks a transition between the Lighthouse (which uses the heptagon as an organizing principle) and the adjacent Bakery (which is based on the pentagon). Dominique is stitching the Marjorie Rice tiling floor covering.

The figure of the baker is being made by Mary and Liz; Liz is making the head and the paws – Liz is our ceramist, she makes beautiful critters – and Mary is making  his whole outfit. Our cat, by the way, is called Arnold. Vladimir Arnold was a famous Russian mathematician who worked on dynamical systems, and to illustrate the stretching and compression in dynamical systems, he worked with a model of a kind of diagonal figure of a cat that got stretched and so on, and that was cut back into pieces to fit back into the square – and everyone  calls that “Arnold’s cat”. So once we made the link with dynamical systems, we knew our baker was  going to be a cat named Arnold. Mary will stitch his name on his  uniform. I hope that Arnold’s students won’t mind too much that we are being a little irreverent here.  

With what other parts of Mathemalchemy are you also involved?

Other parts of Mathemalchemy with which I am involved are, to some extent, the Lighthouse – I  played a role in the mural that will be between the Lighthouse and the Bakery; to some extent, the Integration Hill –I helped design the construction of the hill, with its Lebesgue Terraces and its Riemann Cliffs. But I really like to be peripherally involved with everything – unlike  many of the team members, I am not an expert mathematical crafter, and so I view myself a little bit as an apprentice to everybody who is willing to let me play that role.  

What has surprised you while working on the Mathemalchemy project?

What are the surprises in Mathemalchemy? The biggest surprise is that it works!

Dominique and I had this fantastic idea, and we took her first little model to the Joint Math Meetings, and we hoped that people would be interested, but we weren’t sure, because for artists it is usually a very individual, personal undertaking to create a piece of art, and here we were asking artists to collaborate, in a way  they have never done before. And FOURTEEN people signed up at the Joint Meetings, and then other people  were recruited, and now we have this team of people who are enthusiastic, who collaborate, who really  laugh a lot – in our meetings we make all kinds of puns and talk about this completely imaginary world – it is a lot of fun, and it is wonderful. So that is a big surprise.

And it has been a big, big support for us; we had no idea COVID would hit us, but all of us, I think, enjoy having this group of like-minded, fun people during this isolating period. 

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