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.