Laser Cut Lakes of Wada (and Stand)

The Lakes of Wada is a mathematical construction that produces three plane regions (homeomorphic to a disk) that have a common boundary: all points on the edge of any one of the three regions is also on the edge of both the other regions. The construction is iterative — with the three players (blue, red and yellow) taking turns to grab about 1/3 out of the remaining pink region. Eventually, after infinitely many moves, there is no pink region left, and all points on the boundary of any of the three colours is infinitely close to all other regions.

Together with three friends, we bought four square inches of land in Detroit, and split it between us according to the Lakes of Wada configuration. As a memento, I laser cut the third stage of the process out of four kinds of transparent acrylic and rearranged to give each of us a token with blue highlighting our own part of Detroit.

The stand I hacked together between lasering rounds — it took about 5 rounds with scrap wood, and one failed round with the target acrylic before the design was usable.

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    2 Discussions

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    craftyv

    7 years ago on Introduction

    I agree the colours are great but I have no Maths skills so I'll take your word for it. Beautifull.

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    ChrysN

    7 years ago on Introduction

    I may not understand the math, but it sure looks nice!