Tweet Archive 2022 01
Replying to @henryseg
Looks like there might be an infinite number of circles, in a fractal gasket? At every scale and location there will be a circle that dominates, being the closest integer ratio? (Speculating)
Replying to @henryseg
Like Ford circles. https://en.wikipedia.org/wiki/Ford_circle
Appropriately named. I am reduced to a puddle on the floor. https://www.youtube.com/watch?v=mMTVXDu5v5U
Inspired by Nico Belmonte @philogb to work through the amazing book “Indra’s Pearls”, I’ve extended my Möbius transformation explorer to allow drawing. https://timhutton.github.io/mobius-transforms/
A Möbius transformation is f(z) = (az + b) / (cz + d) where z, a, b, c and d are complex numbers.
Replying to @shizzmd and @philogb
I don’t know anything about electronics, sorry! But please let us know if you work out if there’s a connection.
Replying to @tim_hutton
Whatever you draw (in blue below) is shown multiple times. In green are copies of the sketch under forward iterations of the current transform. In red are backward iterations (iterations of the inverse Möbius transformation).
Replying to @hamish_todd
Frustrated Total Internal Reflection: “The mechanism of FTIR is called evanescent-wave coupling, and is a directly visible example of quantum tunneling.” https://en.m.wikipedia.org/wiki/Total_internal_reflection
RT @davetroy: 1/There are people who are genuinely trying to talk intelligently about cryptocurrencies, but can’t because they don’t have h…
I just followed this to do an LFT and it’s definitely less painful doing the nose swab as he suggests - and more effective.
Also, it sounds like getting a good throat swab too is important with Omicron. https://twitter.com/DrEricLevi/status/1477057391212449793
Using random Möbius transformations to make an IFS fractal. Drag the control points around to explore. https://timhutton.github.io/mobius-transforms/ifs.html
Replying to @tim_hutton
Replying to @tim_hutton
Replying to @tim_hutton
Replying to @AlexandreDizeux
I look forward to seeing the results. I’m sure you can make nicer renders than I did.
Replying to @ericchill
Based on your suggestion I made a button to animate the control points. It’s quite pleasing. Often it just looks cloudy or sparse but there’s always something to look at.
Replying to @Johnicholas
Yes, I often find myself tweaking the control points to get the ends of the black scratches to line up to make dragons like this one. It might be nice to directly drag the scratches themselves.
In Indra’s Pearls they get them to line up mathematically, by thinking about it.
Replying to @rickyreusser
Thanks for making this. I managed to modify it to use the Möbius transformations IFS things I’ve been playing with: https://observablehq.com/@timhutton/mobius-ifs
Replying to @rickyreusser
Looks like it would benefit from a different approach for the color channels. What have people used previously for IFS?
Replying to @rickyreusser
Coloring by the index of the last transform chosen is informative but not yet attractive. :)
Replying to @rickyreusser
Yes, nice. Here I combine the branch value from the last iteration and the one before that:
Replying to @rickyreusser
By keeping a running average of the branch value we get a lot more subtlety:
With 10 billion points and branch coloring we can see a lot more details in these Möbius IFS patterns. Experiment and make your own patterns here: https://observablehq.com/@timhutton/mobius-ifs Thanks to @rickyreusser for the code on which this is based.
https://observablehq.com/@timhutton/mobius-ifs
Replying to @rickyreusser
Have republished with the settings I was using. Works for me on multiple devices, whether signed in or not.
Replying to @AustenLamacraft
It’s the ‘chaos game’: you start with a single point, then at each iteration randomly pick a transformation to apply. The point jumps around and then you can color the locations that it visits. It works with all sorts of transformations. https://en.wikipedia.org/wiki/Iterated_function_system
Replying to @AustenLamacraft
The parameters only change when you drag the control points. Otherwise the only thing changing is the point’s location which is updated each iteration.
A simpler example: go halfway to a random vertex of a triangle: https://en.wikipedia.org/wiki/Chaos_game
RT @JakeArkinstall: @theowl84 @hankadusikova @mknejp Well, it all started when people wanted to std::decay volatile atomics.
Replying to @peterliepa and @rickyreusser
Nice!
Replying to @bulatov_org and @rickyreusser
I’ve added an issue for this because it would be good to achieve. For now you can do it manually by typing JSON.stringify(control_points) into the developer console (F12) and then edit them into the notebook.
Replying to @rickyreusser and @bulatov_org
This is brilliant! I love it.
Replying to @rickyreusser and @bulatov_org
Still a few holes in the random number generation though:
This bot is amazing. https://twitter.com/dreamjobsbot/status/1482617674471464960
Replying to @bulatov_org and @rickyreusser
Yes, although IFS is not the best way to view those sorts of patterns, even with billions of points.
I’m working on a UI for those recipes here: https://timhutton.github.io/mobius-transforms/dfs_recipes.html But it’s early days, there are various issues.
Three views on the same four-transformation Möbius group. Drag the points around to explore: https://timhutton.github.io/mobius-transforms/dfs_recipes.html Now has the DFS drawing algorithm from Indra’s Pearls that shows more of the details than IFS, and a button to export as SVG. ta = 1.86, -0.165 tb = 1.905, 0.06
Replying to @tim_hutton
It’s astonishing that maths should give us gifts like this.
Replying to @MattMarchand_
How do you mean?
RT @rickyreusser: @tim_hutton’s Möbius transform IFS + a randomize button + clicking while watching TV……
Replying to @peterliepa and @rickyreusser
I just noticed that you’re cited in the book for your beautiful videos on Vimeo, eg. https://vimeo.com/4154095
RT @rschu: Volumetric Capture for Matrix 4 🎥
Check out this post breaking down the camera innovations used for @TheMatrixMovie including u…
RT @hollyonthehill: This is ice on my dry sidewalk. I am blown away at its beauty.
Replying to @HirokiSayama
You’re just nerd-sniping us to back-engineer that wordle-style CA: buckminsterfullerene compartmentalization semiautobiographical internationalization immunohistochemistry electroencephalogram magnetohydrodynamics
It took me a while to understand why the rendering of this pattern was going wrong. It was because the fixed points of abAB etc. aren’t on the limit set for these patterns, unlike other patterns in the book.
I have so much to learn. And it is so much fun. #IndrasPearls
Replying to @baabbaash
With oscillators/patterns that change population it might be possible to animate arbitrary short scenes, by changing the density.
Replying to @JasonHise64
From similar thoughts:
https://youtu.be/qh9McOMJL_4
I have an annoying bug in my code. Those straight lines shouldn’t be there. But this will be lovely when it’s fixed. #IndrasPearls
Replying to @sina_lana
There may be one! The line drawing algorithm is a search process, so it could be failing to explore enough. Also I may have pushed the parameters too far in this case, into a region where the patterns degenerate into uncontrolled chaos.
Replying to @sina_lana
It’s not a search of the 2D space, it’s a search of the tree of which of the four Möbius transformations to apply next. The jumps are between branches of that tree. More details in the book Indra’s Pearls.
Replying to @optozorax and @RAnachro
@gregeganSF’s Permutation City and @RealGregBear’s Moving Mars. Two amazing books that make you believe that you really could hack into the source code of the universe.