I learned something fascinating this week! (Unrelated to OP). The algebraic computation of the Hausdorff dimension of a fractal set is *exactly the same* as the Master Equation of the asymptotic analysis of algorithms! I.e.: where a Sierpinski triangle has dimension log(3)/log(2) ~ 1.58—intermediate in between that of a line and of a plane—that's the very same log(3)/log(2) as in the O(n^(log(3)/log(2)) of, say, the Karatsuba algorithm. In Karatsuba, when you recursively split a digit representation of a number in half (2), you get three new multiplications (3). In a Sierpinski triangle, rescaling by a factor of 2 increases the number of non-empty triangles at that scale by 3. And it really is the *same* manipulation: the Hausdorff dimension of the fractal is a critical exponent of an asymptotic function growth rate, a function of the diameters in a covering set in the ε→0 limit.
The first program I spent money on was a fractal app on the Amiga that would allow me to navigate and drive around the fractal using an Atari joystick. So yeah, fractals are core part of compute experience for me
Fractals are due a resurgence, as I recall the Internet used to be about 5% fractals by volume.