Turtles All the Way Down!
Congratulations to Graduate Student Nicole Savir! Her piece, titled "Turtles All the Way Down" was accepted into the juried 2026 Joint Mathematical Meeting (JMM) art show. 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 3^n turtles uniformly scaled by 1/2^n 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 3^n closed boxes of size 1/2^n . As n →∞, the dimension limits to ≈1.585.
Nicole is a first-year PhD student whose primary research interest in Dynamical Systems.
More information about the art show: https://www.ams.org/publicoutreach/math-imagery/2026-exhibition
