Robert Munafo

http://mrob.com/ Concisely: http://mrob.com/pub/math/numbers.html The rest of the site it's amazing too.

As an adjunct to this, if large numbers interest you there's a really excellent and long-standing set of pages about them at http://www.mrob.com/pub/math/largenum.html which has some fascinating incidental detail and covers infinities as well as large finite numbers.

Reminds me of the Gray-Scott explorer [0], implemented with WebGL (in 2012!!). Mathematics is beautiful! [0] https://www.mrob.com/pub/comp/xmorphia/ogl/index.html

Read http://mrob.com/pub/math/largenum.html . After that you'll probably look easier to those numbers.

There used to be a site called the Inverse Symbolic Calculator (also a sibling site, Plouffe's Inverter) where you could give in a decimal expansion and it would search for known constants. Unfortunately, it seems to be down (the frontend exists, the backend just gives 404). Maybe someone else made something similar? Edit: I found https://mrob.com/pub/ries/, which may or may not help.

See also this older LEGO orrery produced by the University of California as an educational project for NASA Kepler mission: https://www.nasa.gov/wp-content/uploads/2016/09/table-top_transit_demo… https://www.nasa.gov/wp-content/uploads/2016/09/table-top_transit_demo… Also: http://mrob.com/pub/lego/orrery.html

Not really a place. I think the technical term is thing. You can argue it's a real thing but not very place like. Seahorse Valley is more place like if you want to debate the reality of these things https://www.mrob.com/pub/muency/seahorsevalley.html

>Is backwards compat a thing on osx? There was a time when it was --- there was a "Missile Command" game written for the 128K Mac which still ran fine in the Mac OS environment running the last version of MacOS on PowerPC machines: http://www.mrob.com/pub/comp/missile20.html and the previous version of Rosetta was for running PowerPC apps on Intel machines (and before that it was for handwriting recognition). and I've always regretted that Macromedia Freehand didn't get re-written so as to run for longer --- that's one of the reasons I've pretty much switched to a Windows machine (using a Samsung Galaxy Book 3 Pro 360, which replaced a Book 12, which replaced a Toshiba Encore 2 Write 10, which replaced an Asus Vivotab Note 8, which replaced a Fujitsu Stylistic ST-4110, which replaced an ST-2300, &c.) I use a Wacom One w/ my MacBook, but it's just not the same.

Can't raise this topic without mentioning the Large Numbers Page: http://www.mrob.com/pub/math/largenum.html With this link being particularly relevant: http://www.mrob.com/pub/math/largenum-10.html

I'm not sure whether this list is only for CA's, but I'm gunning for 'U-Skate World' (a specific set of coefficients on the Gray-Scott reaction diffusion) to one day hopefully have a chance at being shown to be turing-universal: https://mrob.com/pub/comp/xmorphia/uskate-world.html I've also found some things that I thought looked and behaved vaguely 'game-of-life-like' in other formulas in Ready: https://youtu.be/W6sO8ZkgU9s

Looks similar to the Gray-Scott model. https://mrob.com/pub/comp/xmorphia/

http://mrob.com/pub/comp/xmorphia/ogl/index.html very hypnotic:)

Nice to see a mid-90's page still up: http://mrob.com/pub/comp/xmorphia/

Or this page [1] on large numbers. [1] https://mrob.com/pub/math/largenum.html

Related: Robert Munafo's RIES [1] tries to synthesize increasingly complex formula which solution is a given number. [1] https://mrob.com/pub/ries/

You can generate these SmoothLife patterns with Ready [0] [0] https://github.com/GollyGang/ready/blob/gh-pages/Patterns/SmoothLife20… I find USkate the most beautiful, http://mrob.com/pub/comp/xmorphia/uskate-world.html

ObXkcd: https://xkcd.com/1047/ and https://mrob.com/pub/ries/index.html

No, I want Apple to do what they've done in the past and get Intel to do something for them. http://mrob.com/pub/comp/mac-models.html#intel_special

Right now FractalViewer is using a modified version of the Successive Refinement algorithm invented by Robert P. Munafo. See a description of the original algorithm http://mrob.com/pub/muency/successiverefinement.html . Version 2 of FractalViewer will use Web Workers (multipple threads) to render the image, so it will resemble "the maps one" (rendering multiple smaller squares at once). See progress on this at https://github.com/valera-rozuvan/FractalViewer/issues/3 . By the way - maybe I got your question wrong. What do you mean by "a render technique like the maps one"? Can you point me to a resource where it is described?

Reaction-diffusion could easily generate these patterns. There are several places in parameter space that look possibly correct. http://mrob.com/pub/comp/xmorphia/index.html

Technically incorrect: http://mrob.com/pub/math/largenum-2.html

On the flip side of the coin, there's ries, which takes a number and finds a mathematical expression that approximates it: http://mrob.com/pub/ries/

I prefer RIES [1], that does pretty much the same thing. You can download its source code (C, GPL licensed) [2] or try it on the webpage. Oblig. (relevant) xkcd [3]. [1] http://mrob.com/pub/ries/index.html [2] http://mrob.com/pub/ries/src/ries.c.txt [3] http://xkcd.com/1047/

This explanation of the work the automata rule needs to do was interesting: http://mrob.com/pub/math/quad-grid-glider.html (from g+)

This work is subtly related to chaos theory. The nth coefficient of the ith Mandelbrot polynomial lemniscate [3] is equal to the number of possible binary trees with n nodes of height i or less. This is because z -> z^2 + c reflects coefficients recursively produced by repeated applications of the binomial theorem. When n becomes <= i, the nth coefficient stabilizes, converging to the nth Catalan number, which is the number of possible binary trees with n nodes. The nth Catalan number is also the number of triangulations of an n+2-gon. https://en.m.wikipedia.org/wiki/Catalan_number#Applications_in_combina… Now, there is a 1-to-1 bijective mapping between binary trees of height n and node count i, and n+2 sided polygon triangulations with i segments. https://www.r-bloggers.com/2015/07/catalan-numbers-fortriangulationsga… In fact, the same associahedron in "Flipping until you are lost" is mentioned here: https://www.researchgate.net/figure/The-bijection-between-binary-plane… What is the significance of all of this? There is currently no closed form approximation for these numbers. As simple as it might sound, we have no closed form for the number of binary trees with i nodes of height <= n. If we did, we could approximate the Mandelbrot and it would unlock new frontiers of understanding chaos theory. Philippe Flajolet, a now-deceased titan of analytic combinatorics [2] wrote some papers on the…

There's a numberphile video on that I just watched: https://www.youtube.com/watch?v=6ltrPVPEwfo I really don't like this formula. The numbers grow absurdly huge really quickly, and the only way of finding A is brute force search (and there are multiple possible values, they just pick the smallest that works.) It's like saying the number 0.235711131517... contains information about all the prime numbers. Well it does, but once you see how it's constructed it's not terribly interesting. Anyway I think you are saying that the constants might have low kolmogorov complexity. That is, the constant could be compressed to many fewer bits of information. That seems unlikely. There's no reason why constants can't be arbitrary or random. Perhaps there are many universes and each has a different constant. And trying to fit an expression to them is impossible, because we only know them to a few digits. That's not anywhere near enough information, and any expression like that will almost certainly be overfit. But if you insist you could try RIES: http://mrob.com/pub/ries/ries.php?target=1836.15267389&rst= None of the formulas get out more characters than they put in, or even get more than a handful of digits. It's indistinguishable from a purely random number.