In real world computers, we have finite memory, so my reading of this was assuming a finite state space. The fractal stuff requires an infinite sets, where two notions of smaller (‘is a subset of’ and ‘has fewer elements’) disagree—the mini-fractal is a subset of the whole fractal, but it has the same number of elements and hence corresponds perfectly.
In real world computers, we have finite memory, so my reading of this was assuming a finite state space. The fractal stuff requires an infinite sets, where two notions of smaller (‘is a subset of’ and ‘has fewer elements’) disagree—the mini-fractal is a subset of the whole fractal, but it has the same number of elements and hence corresponds perfectly.
What about quines?