Timeline for Largest number N for which injective mapping $f: 2^N \to 2^8 \times 2^8 \times 2^8$ which is Lipschitz-1 CT with $K\leq 3$ exists
Current License: CC BY-SA 4.0
7 events
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Mar 4, 2021 at 21:59 | vote | accept | polpetti | ||
Feb 2, 2021 at 4:34 | comment | added | polpetti | @WillSawin Good suggestion about the Hilbert curves! I've added some colormaps from 3D Hilbert Curves in my answer | |
Jan 31, 2021 at 15:16 | comment | added | Will Sawin | Are you sure you want Lipschitz continuity? For $x$ continuous and $f(x)$ discrete, you are always going to have arbitrarily small changes in $x$ leading to changes in $f(x)$ (if $f$ is constant). Maybe you discretize $x$ before checking the Lipschitz condition, but then it only depends on $| f(x + 1/2^N) - f(x)|$. A Holder continuity condition might be more useful here because it forces $f(x_1)$ to stay close to $f(x_2)$ for longer. If you were saving $x$ into two numbers instead of three, would a Hilbert curve (en.wikipedia.org/wiki/Hilbert_curve) be what you want? | |
Jan 30, 2021 at 22:04 | answer | added | polpetti | timeline score: 0 | |
Jan 29, 2021 at 7:20 | review | Close votes | |||
Jan 31, 2021 at 15:20 | |||||
Jan 29, 2021 at 5:37 | review | First posts | |||
Jan 29, 2021 at 7:02 | |||||
Jan 29, 2021 at 5:32 | history | asked | polpetti | CC BY-SA 4.0 |