Tegmark's Level I multiverse needs no exotic physics — only two mundane facts: space is (plausibly) infinite, and any bounded region can hold only a finite number of distinct particle arrangements, because it has finite energy and finite volume (a Bekenstein-bound argument caps its entropy, hence its number of microstates N).
Regions with the same macrostate -> same N possible microstates
Birthday-paradox estimate for the first repeat:
k* ~= sqrt(pi/2 * N) ~= 1.2533 * sqrt(N)
P(at least one repeat among k regions):
P(k) ~= 1 - exp( -k(k-1) / (2N) )
This simulator makes N tiny (8–400) so the repeats happen on-screen in seconds. In the real universe N is roughly the number of quantum microstates in a Hubble volume, of order 10^(10^118) — astronomically larger, but still finite — so the same birthday-paradox logic implies an identical copy of our observable universe exists, just unreachably far away (Tegmark's own estimate: roughly 10^(10^118) metres).
- N slider — how many distinct arrangements a region can hold; smaller N forces repeats sooner (a smaller "alphabet" to draw from).
- Lattice size — how many Hubble volumes are laid out along each axis (grid² total regions in this 2D cross-section).
- Reseed — draws a fresh random arrangement for every region with a new seed, like sampling a different slice of an infinite universe.
- Show: all pairs / nearest only — toggle between every duplicate pair found, or just the closest one to the centre region.
- Zoom / drag — a real infinite universe can't fit on one screen either; pan and zoom to inspect distant regions of the lattice.
- Histogram panel — the count of regions landing on each of the N arrangements; a taller bar than its neighbours is a visible duplicate cluster.
Real-world relevance: this is the same combinatorial argument used in cryptographic collision attacks (the "birthday attack") and in estimating hash-function collision rates — cosmology, quantum computing and cryptography all lean on the identical sqrt(N) scaling law.