Pinned toot

This predates my Mastodon accounts but it ought to be on here so here it is: my interactive blog about the domino computer.

This week I built the Mercator Rotator.

Mercator maps famously make Africa small and Greenland big, but by changing which way around we apply the projection we can make any place we like any size we like. Spin the globe, and see what you can create.

https://scholar.social/@bgcarlisle/101535435026541826

Spoilery discussion of my solution

Then I wrote the N=8 version in binary and it clicked and I felt simultaneously like a genius and an idiot.

Spoilery discussion of my solution

Then I drew out some coloured tesseracts for low-N cases and that worked well. I found you could step up to the next solution by pulling out a copy of the solution into some new dimension, giving it N new colours, and then pulling out as many permuted versions as you need to fill in the missing flips β but it didn't give me an algorithm to devise the permutations.

Spoilery discussion of my solution

I got hung up for ages on parity β because every possible arrangement you can reach by flipping one coin has the same parity, the 8x8 chessboard can be modelled as colouring a 63-dimensional cube, rather than a 64D one. Somehow I thought the loss of that one dimension would be more useful than the nice factorisability of 64. No idea why. And you can get to it that way but it's inelegant.

Finally cracked this puzzle over lunch today. Very satisfying, I think it's the first one of these Big Hard Logic Puzzles I've solved start to finish on my own.

This also means I'm no longer messing up Matt's viewer retention stats from having paused it a week ago pretty near the beginning. I'd be interested to see the drop-off in the graph at the point when they say "pause the video now and have a go at it".

@andrewt As if this weren't all confusing enough, I believe the set of points depicted here is what's technically known as collielinear.

@andrewt It's the prefix col- which sometimes occurs in latin-derived words instead of co- or com- with base words that begin with an 'l'. You see it in "collateral" and "colloquial" and even in "college" and "collegial." That said, I think the one-l version, "colinear" is widely accepted as correct these days.

Someone posted a gif of this effect on birdsite and I wanted to understand it so I've built it as a space-warping raymarcher.

Its some lovely maths that I think I *mostly* understand now:

Manchester MathsJam regular and occasional tamed programmer for the Nerds

Joined Apr 2018