Blog – GMU Math MakerLab

3D Printing of Invariant Manifolds in Dynamical Systems

Stability of Floating Objects at a Two-Fluid Interface

Mathematics of Floating 3D Printed Objects

3D Printing Data

Turtles all the way down accepted to math art show

Turtles 3D print

Nicole Savir of the Math Makerlab has had an art piece accepted to the JMM 2026 Mathematical Art Exhibition.

Turtles All The Way Down

by Nicole Savir

The print references an anecdote by mathematician Bertrand Russell, where a woman suggests the world sits on a giant turtle, and when asked what the turtle stands on, she responds: “It’s turtles all the way down!”

The turtles were born from an adaptation of Dr. Sander’s direct recursion code via OpenSCAD. Defining the system f= f₁ ∪f₂ ∪f₃, where for each iterate n, the functions generate 3ⁿ turtles uniformly scaled by 1/2ⁿ in each dimension and translated by vectors. We define our limiting turtle set as T. T has an uncountable number of turtles and each limiting turtle has infinite turtles underneath. The fractal dimension of T is determined by covering T with 3ⁿ closed boxes of size 1/2ⁿ . As n →∞, the dimension limits to ≈1.585.

Modeling Dynamical Systems for 3D Printing

Stephen K. Lucas, Evelyn Sander (of the GMU Math Makerlab), and Laura Taalman wrote an article about how to practically 3D print actual physical models of such dynamical structures. This appeared in an article in the American Mathematical Society Notices in December 2020 (cover image shown is a 3D printed model from the article). An adapted version appeared in the book The Best Writing on Mathematics 2021, Princeton University Press.