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 fₖ generate 3ⁿ turtles uniformly scaled by 1/2ⁿ in each dimension and translated by vectors. We define our limiting turtle set T=∩f⁽ⁿ⁾(t), with t=initial turtle. T has an uncountable # 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→∞, {ln3ⁿ/ln2ⁿ}→ln3/ln2≈1.585.