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Dynamics of flows and maps (continuous and discrete time), including infinite-dimensional dynamics, Hamiltonian dynamics, ergodic theory.

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A one dimensional fractal like set with the same line width within a bounded area? [closed]

Say that we have a line $\left(0,0.5\right)$. I want a process that can split that line and half and move that half a bit, and then take half of that half and moved it and so on, so that by the end al …