Posts by OscarCunningham@mathstodon.xyz
(DIR) Post #APnVFOkISDNKL7aunI by OscarCunningham@mathstodon.xyz
2022-11-20T07:59:45Z
1 likes, 2 repeats
Amazing new result about Conway's Game of Life! You can build anything you want by colliding 15 gliders together: https://b3s23life.blogspot.com/2022/11/in-conways-life-fifteen-gliders-can.html⬛⬜⬛⬛⬛⬜⬜⬜⬜This result was a long time in the making. Read the article to find out how it works, and why 'anything' is not actually everything.This blogpost breaks down the construction even further: https://btm.qva.mybluehost.me/building-arbitrary-life-patterns-in-15-gliders/#Math #Mathematics #Maths #CellularAutomata #Conway #GameOfLife #ConwaysLife
(DIR) Post #APnVFPiuoprfN7xKHQ by OscarCunningham@mathstodon.xyz
2022-11-20T10:10:56Z
0 likes, 1 repeats
@johncarlosbaez Anything that can be constructed by colliding (any number) of gliders can be constructed by colliding 15 gliders. However we know there are patterns that can't be constructed with gliders. These include 'Gardens of Eden' https://conwaylife.com/wiki/Garden_of_Eden which have no predecessor whatsoever under Life's rule. But it's also now know that there are interesting patterns such as still-lifes that can't be constructed https://cp4space.hatsya.com/2022/01/14/conway-conjecture-settled/.
(DIR) Post #APpoo9EWN9s6jVlSPg by OscarCunningham@mathstodon.xyz
2022-11-21T17:03:53Z
0 likes, 0 repeats
@mastodonusercount That spike was hiding a real increase.
(DIR) Post #ARcjlSxcAPcf9oyvFQ by OscarCunningham@mathstodon.xyz
2023-01-13T14:04:56Z
0 likes, 1 repeats
Has anyone written an explanation for category theorists of how monads are used in programming? All I can find are guides for programmers that assume you don't know any category theory.
(DIR) Post #ARrJziiShYgmdiQfx2 by OscarCunningham@mathstodon.xyz
2023-01-20T14:46:20Z
0 likes, 0 repeats
@EricZhang456 This is how Docker containers feel.
(DIR) Post #ATz0D1WrI1Kh8OH8D2 by OscarCunningham@mathstodon.xyz
2023-03-22T02:28:24Z
0 likes, 0 repeats
@divbyzero I wonder if it's possible to tile the plane and then three-colour the tiling so that no adjacent regions have the same colour?
(DIR) Post #ATz0D33ranKNt2j0IC by OscarCunningham@mathstodon.xyz
2023-03-25T08:58:25Z
0 likes, 1 repeats
@divbyzero The aperiodic 'hat' tilings seem to have a four-colouring where one of the colours consists of precisely the 'flipped' tiles.Even more amazing, when I was trying it I never had to make any choices after the first four colours. My moves were always forced. So it seems like this is a natural unique colouring. Wonderful!I just tried this by hand, I don't have a proof that it extends forever.
(DIR) Post #ATz0DEigFNVu2ouFwO by OscarCunningham@mathstodon.xyz
2023-03-25T09:22:52Z
0 likes, 0 repeats
@divbyzero Jesse Clark (@myhf) points out that when four tiles meet at a point they still have all different colours. https://twitter.com/myhf/status/1639053012399439872?s=20
(DIR) Post #ATz0DErXiQbQUJ3Kkq by OscarCunningham@mathstodon.xyz
2023-03-25T08:59:30Z
0 likes, 0 repeats
@divbyzero This has practical applications for mathematics departments undergoing renovation.
(DIR) Post #Aap2usc7C9Fel2Om9I by OscarCunningham@mathstodon.xyz
2023-10-15T20:25:50Z
0 likes, 1 repeats
#Mathober #Mathober2023 The prompt for day 11 is 'Quadratic'.When I was a kid, my mum would buy The Guardian newspaper, and along with the crosswords and sudokus there was a section of maths/logic puzzles.I remember one of these puzzles asked the following question: 'Suppose we throw a coin onto a tiled floor. The tiles are squares with side length twice the diameter of the coin. What's the probability that the coin avoids landing on a crack?' (I'm sure they presented it more entertainingly than that.)Now this problem doesn't require you to solve a quadratic. But when I worked out the answer I remember thinking that the probability was much smaller than I expected. It's hard to avoid those cracks!So I thought it might make a fun game. You'd scale up the tiles until there was just less than a 50% chance that the coin missed the crack. People would think it was an easy game, but they'd lose more often than they'd win. (I suspect there is no possibility at all of skillfully controlling the bounces of a metal coin on a hard floor.)To do this you'd have to find the tile size at which there was a 1/2 chance of landing on a crack. This inverse problem *does* require you to solve a quadratic. I remember it as one of the first times I used some 'advanced' maths to solve a problem that I'd thought up myself, rather than one I'd gotten from a book.#Math #Maths #Mathematics
(DIR) Post #AbGQknJtzeP8GU67ua by OscarCunningham@mathstodon.xyz
2023-10-29T13:45:14Z
0 likes, 0 repeats
@ParadeGrotesque Yes, a level 3 enemy does 0, 1 or 2 damage each hit, while a level 4 enemy does 0, 1, 2 or 3. So with two 🛡️ you're invunerable to 🐗 and 👻, and 👹 and 🐺 can only do 1 damage to you if they roll max.The 🍄, 🌰 and 💎 are just collectables with no effect.
(DIR) Post #AdIc4lYNImuNu2p6Ey by OscarCunningham@mathstodon.xyz
2023-12-29T10:46:07Z
0 likes, 0 repeats
@horhik I think if ω is a 1-form then ω∧ω will always be 0, which doesn't feel very kawaii. But if ω is a 2-form or higher then we're okay.
(DIR) Post #AdIvSDLs0rYnuJrvYO by OscarCunningham@mathstodon.xyz
2023-12-29T14:23:15Z
0 likes, 0 repeats
@horhik I think what I said is true. That's the alternating property of the exterior product.
(DIR) Post #AdVTuhPM7R7zhj0ZY8 by OscarCunningham@mathstodon.xyz
2024-01-04T09:23:44Z
0 likes, 0 repeats
@ColinTheMathmo I remember thinking the moon looked very neat this morning. 🌗
(DIR) Post #AjA1XAomoRevvrZPU0 by OscarCunningham@mathstodon.xyz
2024-06-21T17:40:57Z
0 likes, 0 repeats
Got this @gregeganSF classic for my birthday! Have heard many good things about it so I'm excited to read it.
(DIR) Post #AlDfoP9mPmbyECcNou by OscarCunningham@mathstodon.xyz
2024-08-22T06:37:47Z
0 likes, 1 repeats
Why is it called 'majority logic decoding' and not 'the median is the message'?
(DIR) Post #Aw5BFNYJD4DDUpEem0 by OscarCunningham@mathstodon.xyz
2025-07-12T06:17:30Z
3 likes, 2 repeats
'poly-' means many'-est' means most'-er' means more'polyester' lots and lots and lots and lots
(DIR) Post #AxIOAFAhHSQgFhzZKq by OscarCunningham@mathstodon.xyz
2025-08-18T11:18:23Z
1 likes, 0 repeats
A working QR code in the style of Piet Mondrian. Inspired @divbyzero and @andrewt.#Art #PietMondrian #QRCode
(DIR) Post #AxLHX3JnOsbFwh3Ziq by OscarCunningham@mathstodon.xyz
2025-08-19T14:31:57Z
0 likes, 0 repeats
@kenshirriff Actually most of the data is in the black grid! This image shows how it works.
(DIR) Post #AyEHgMLDTlXB88acW8 by OscarCunningham@mathstodon.xyz
2025-09-15T11:36:58Z
0 likes, 0 repeats
@robinhouston This reminds me of the time as a kid I was at a chess tournament. The local journalist *insisted* that we rotate the board 90⁰ so that the fold in the board wasn't visually distracting in the middle of the photo.