Tortoise – Fabrication

Tess the Tortoise

Tortoise

Fabrication

Tess the Tortoise

Tortoise’s Story

The outline of the Tortoise’s story, and the different concepts highlighted in it, were formulated by Jessica K. Sklar. This was a component that crystallized early on—it was essentially adopted as conceived.

Read Tess the Tortoise’s Story by Jessica K. Sklar

Preliminary sketch: Tess with a torus balloon
Preliminary sketch by Jessica K. Sklar.
Tortoise photograph by Amoury Laporte, pix.alaporte.net.
Jessica K. Sklar meeting Tess “in person” for the first time.

Tortoise’s Shell

Tess’s ceramic shell was crafted by Liz Paley. She threw a flat clay disk, and after it stiffened to a “soft leatherhard” stage, she used a serrated tracing wheel to impress the clay with a heptagonal tiling of the hyperbolic plane. Then she gently nudged and stretched the disk into a shell shape more befitting a tortoise.

  • Shell of the Tortoise

Tortoise’s Body

Tess’  body was knit by Kim Roth. The body was knit in seven main pieces: the top and the bottom of the body, the four legs, and the head/neck. The bottom of the body was knit in two colors to mimic patterns found on tortoise bellies. The toes on the feet were all knit individually and then knitted together to start each leg. 

The tortoise was assembled on an armature wire frame designed to fit the shell, and stuffed with polyfill. The tail was knit on after assembly and the shell was put on. Due to the armature wire, the tortoise stands on its own and is posable.

Read How to knit a Tortoise in n+1 steps by Kimberly Roth

Tess the Tortoise

Zeno’s path

Zeno’s path was designed by Edward Vogel and Ingrid Daubechies and sewn by Dominique Ehrmann.  Originally, the design was that the constant-width path would showcase the division in half the length, followed by a quarter-length, etc., by using different pavers on the different segments, with each paver exactly half the area of the previous one, and the same number (14) of whole pavers for each segment. But then exuberant Tess came out a bit wider than expected, so that the path had to be widened at the start, and the pavers were adapted accordingly.

Zeno’s path was designed by Edward and Ingrid and fabricated by Dominique
Sewing Zeno’s path by Dominique Ehrmann

In the installation, the ratio between the areas of pavers in neighboring segments is therefore no longer the aimed-for factor 2. But maybe this is just our rationalization—maybe this piece of the wonderland has a peculiar relativistic geometry, in which the width measurements change as Tess progresses. Not that Tess cares about measuring widths—she is just enjoying her walk.

Preliminary sketches: Zeno's Path arch
Preliminary sketch of the Arch of Zeno’s path

Arch to Zeno’s path

The arch marking the entrance to Zeno’s Path was sketched by Jessica, designed by Dominique and constructed by Ingrid.

Sierpinski kite of Tess the Tortoise

Kite

The frame for the kite was soldered with brass rods by Bronna Butler, and the fabric cut and attached to the frame using Mod Podge® by Ása Jóhannesdótttir, Kim, Jessica, and Carolyn Yackel.

Mod Podge® is a registered trademark of Plaid Enterprises of Norcross GA, United States

Dominique Ehrmann and Edward Vogel discussing the installation of the (frame of the) kite
Dominique Ehrmann and Edward Vogel discussing the installation of the kite (practically dred)
Jessica assembling the Riemann wall

Riemann wall

The Riemann wall was designed by Jessica and its components were cut from pine wood by Gavin Smith.

Jessica in front of the Riemann wall in Mathemalchemy

Signalisation and lists

The Hilbert’s Hotel billboard and to-do list were designed by Jessica, drawn by Dominique, modified by Bronna, and printed onto paper which was then laminated.

Draft of Tess's to-do list
Tess the Tortoise
Tess the Tortoise and her to-do list
Hilbert's Hotel Sign
Hilbert’s Hotel billboard drawned by Dominique Ehrmann.
Hilbert’s Hotel billboard on the Riemann wall

Integral hill

The original idea of Lebesgue Terraces and Riemann Cliffs for Integral Hill was Ingrid’s.

Dominique drew the shape of each of the Lebesgue Terraces (making sure they were mathematically acceptable level curves of a univalued function of 2 variables), Ingrid vectorized them, and they were executed in wood by Gavin Smith and Albert Kennett.

Dominique’s drawing of the Lebesgue terraces
Integral hill on Dominique's maquette
Integral hill on Dominique’s maquette
Quick assembly before covering the terraces with fabric
Quick assembly before covering the terraces with fabric

Attaching the green fabric onto the Terraces was an “all-available-hands” task orchestrated by Dominique during the first phase of the construction in July 2021. The 213 (!) spacers between the Terraces were lovingly coated in fabric by Elias Zauscher.

Riemann Cliffs

To make the Riemann Cliffs we purchased over 300  hexagonal dowels of 1” diameter and 20” long. Stefan Zauscher took on the woodworking task of gluing and cutting until we had dowels of approximately the right length, in 5” increments, and those were then hand-marked by Ingrid to indicate more varied heights that would look natural yet still suggest a (noisy) height graph of a reasonable function.

Assembly sketch of the Integral Hill

The final cutting, gluing together of all the columns and the painstaking assembly into balanced blocks, which would make the mountains easy to assemble in future, was taken on by Stefan, Liz, and Li-Mei Lim.

The cliffs were finished with acrylic paint by Tasha Pruitt.

Koch Snowflakes

The snowflakes were designed by Ingrid and Edward—some of them are iterations of Koch’s original construction; others have slightly adapted coefficients to make more varied shapes. In some of the snowflakes, smaller designs of lower-order iterations are engraved; others have tiny snowflake cutouts. The designs were prepared for laser cutting by Edward, and then executed by Panoko).

Read Snowflakes and Lasers by Edward Vogel

Tasha Pruitt then painted some using an airbrush and acrylic paint, sanded others, and varnished them all with either a clear gloss or matte coat.

A mobile was constructed by Stephan and Liz Paley.

Koch Snowflakes

Read more about the Tortoise

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