Tom Lowe

I'm interested in Computer Graphics, Geometry, Mathematics and Physics. I have worked in Games Development, Animation Development, and now in Robotics Development, I guess that makes me a developer.
Vous pouvez me parler dans n'importe quelle langue, c'est assez facile à traduire en ligne si je ne le connais pas.

website: https://sites.google.com/view/tom-lowe-projects
My shaders: https://www.shadertoy.com/user/TGlad
book: https://www.worldscientific.com/worldscibooks/10.1142/11219?srsltid=AfmBOoqqqUWnFXTmu46XjB_s6yfU0FbPyFjAD3oi5n1HQgFPPMyxrkHp#t=aboutBook
inversive limit sets: https://www.shadertoy.com/view/wcBSzR

Public Key

npub1jj2r7pa3qvunqjaw8z7yl23ee24y9dg9qnx9v5gzdjtn6e4ujdgs6pjlmk

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toml_at_mathstodon.xyz@momostr.pink

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nprofile1qqsff9plq7csxwfsfwhr30z04guu42jzk5zsfnzk2ypxe9eav67fx5gpz3mhxue69uhhyetvv9ujuerpd46hxtnfduqs6amnwvaz7tmwdaejumr0dsctm7mk

Publishing to

relay.damus.io

nos.lol

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Last Notes

2026-10-21 00:14:06 UTC

I was reading this piece about fractal art in a Marvel movie https://www.fxguide.com/fxfeatured/the-fractal-nature-of-guardians-of-the-galaxy-vol-2/
and came across this nice animation of a variant of the 16-cell void-sponge that I use in my locomotion demo: https://www.shadertoy.com/view/33cfDl
I'm not sure what sort of variant it is, and might even be a 24-cell limit set. But what interested me is that it flattens the cube shape into more of a cylinder shape, using an edge centre (1,1,0) surge (hyperbolic Mobius transformation). Could this be used to demonstrate a different form of locomotion?
(1/2)
https://media.mathstodon.xyz/media_attachments/files/117/475/947/295/637/019/original/8a6750899ab65286.mp4

2026-09-07 22:13:19 UTC

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it's non-renewable but it's an infinite resource. We should also consider the growing ability of AI to help us understand the problems; as an explanatory tool for other peoples' and its own proofs.

2026-08-26 23:01:50 UTC

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"At some point AI may be better at math than humans in all ways."
That would be like saying that a calculator is better at maths than humans. It is true in a sense, but we shouldn't personify AI, it has no drive and motivation. The best results in future will come from mathematicians that are adept at using AI to help them, and in optimising the network design. That includes optimising results per KWh.

2026-08-25 22:48:02 UTC

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according to gemini it is about 7 days or a big longer. I thought it would be way shorter.

2026-08-20 04:55:09 UTC

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Geez, it's travelling at 8% of the speed of light!

2026-06-04 07:53:32 UTC

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I agree that LLMs are not conscious, but I disagree with the suggestion in the title as I see no reason why AI in some form couldn't be conscious at some point.
Not LLMs training on texts but by evolving in a virtual environment that requires emotions and awareness to persist.

2026-05-22 01:45:48 UTC

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this story makes me think that public AI angst comes down to how results are reported.
Instead of language like "AI beats humans, AI outsmarts best mathematicians" etc, the reporting should be "Human ingenuity doesn't just prove maths problems, it comes up with automata that auto-prove problems. Mathematicians are advancing their field by training algorithms to prove at a large scale".
The people who continue to develop these creative techniques should be awarded as top mathematicians, rather than treated as a few engineers who stumbled on something, while giving "AI" the credit. Machine learning theory is advanced mathematics.

2026-04-16 10:52:12 UTC

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as an aside the boiling frog effect is most likely fake. Nobody has ever reproduced it since the original experiments. Frogs jump out of hot water, even if its temperature is raised very slowly.

2026-03-29 05:21:14 UTC

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Without adding new limit sets, we can finesse how a limit set links to its destination set. In this case I'll adjust how the smooth planet limit set links to the crater (shell-shell) limit set.
Firstly you can choose which generating sphere in the planet set connects to which sphere in the destination. But you can also choose to link any 'descendant' planet sphere to the crater sphere.
Here the planet's 5th sphere's child sphere 0 links to the crater, rather than just the planet's 0th sphere.
(3/4)
https://media.mathstodon.xyz/media_attachments/files/116/310/778/614/971/968/original/211e7dad6cee64ca.png

2026-03-29 05:15:37 UTC

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If we apply this to a mainly spherical limit set then we get patches of craters over something more like a planet or moon.
The craters are mixed with the smooth planet limit set, so you get two terrain types. And of course the craters have the bushes down the bottom.
https://media.mathstodon.xyz/media_attachments/files/116/310/750/402/600/580/original/8e40cd88cfc7fb4c.png

2026-03-29 05:11:40 UTC

This odd shape is a shell-shell (cratered surface) inversive limit set made of six spheres in an octahedral arrangement.
The top sphere links to a cluster-sponge (programmer art for something like bushes, let's call them alien bushes).
You can see that noy only is the top half vegetated, but it places this vegetation in the other hollows too, as though there's a bit of shelter or water down there.
(1/4)
https://media.mathstodon.xyz/media_attachments/files/116/310/739/628/992/737/original/5c01f55505022ee2.png

2026-03-07 22:34:31 UTC

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I interpreted it that she is looking straight at us and in the mirror she is looking at the customer therefore we are the customer.

2026-01-20 10:16:30 UTC

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ooh, a fancy number, thanks.

2026-01-20 08:32:38 UTC

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the sine function looks very similar to the standard one. But larger multiples give some nice patterns. Does anyone know the exact coefficient for the bottom ∞ shape?
higher def: https://tglad.blogspot.com/2026/01/parametric-functions.html
(2/2)
https://media.mathstodon.xyz/media_attachments/files/115/926/488/005/391/080/original/8f3d213f01155037.png

2026-01-20 08:27:53 UTC

If you graph a function by integrating its gradient as an angle then several functions like tan 𝑥 and 1/𝑥 become continuous.
Nothing very unusual here, but I hadn't seen them in this form before.
(1/2)
https://media.mathstodon.xyz/media_attachments/files/115/926/459/241/783/267/original/a2a23d526ea7f4ec.png

2026-01-14 23:19:15 UTC

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and there's also the recent approach using Finsler gravity: https://iopscience.iop.org/article/10.1088/1475-7516/2025/10/050
I wonder whether string theory can accommodate the Finsler adjustment to GR.

2026-01-01 12:14:33 UTC

The void-sponges that I made in this post (https://tglad.blogspot.com/2024/10/void-sponges.html) have the nice property that they are symmetric to Mobius transformations that rotate around a circle. They act much like projected 4D polytopes even though they are 3D structures.
This has the interesting property that the structure could "swim" through water, since its conformal motion is wider on the part pushing down and smaller on the part going up.
(1/3)
https://media.mathstodon.xyz/media_attachments/files/115/819/780/038/941/696/original/51579c5bd7135a57.mp4

2025-12-22 17:37:50 UTC

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asking politely for no more addictive algorithms is like asking politely for the tobacco industry to go away. Addiction sells in an unregulated market.

2025-12-12 10:08:52 UTC

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I don't know, but the optimally gravitating homogenous shape is interesting: https://arxiv.org/abs/1412.5541
Points on your convex shape that are less like this would be less gravitating.

2025-11-19 23:56:33 UTC

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"I knew that science popularizer Lawrence Krauss was a sex pest and a creep."
I didn't know that. Though from some of his interviews he comes across as a little bit full of himself.
I also found his work slightly disengenuous - Universe From Nothing, and the recent 'universe is not a simulation' paper.

2025-11-19 00:31:06 UTC

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anyone know what he means by "each spatial dimension is actually 3 dimensions"? I'm familiar with fibre bundles and direct products etc but I don't think that's what Hamilton means.
Maybe he means that every point in x has two extra microscopic dimensions.

2025-11-12 23:29:28 UTC

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Interesting. There is an old paper that shows that complete frame dragging can occur inside a particular mass shell that is ellipsoidal. Now I'm wondering if it is the same one, I'd have to re-read.
https://iopscience.iop.org/article/10.1088/0264-9381/2/6/015/pdf

2025-10-31 12:09:30 UTC

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that's a weird discovery. An ellipsoid of revolution would be basically the same as the ellipse string method. I didn't expect the nonuniform ellipsoid to be quite such a strange extension.

2025-10-19 12:09:10 UTC

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would make a great front cover for a sci-fi book.

2025-09-30 00:15:25 UTC

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reminds me of an old thought about dark matter. What if dark matter repelled itself gravitationally, but was attracted to normal matter gravitationally.
I don't think negative mass could achieve that combination though.

2025-08-19 06:46:33 UTC

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I suspect it is more than that, but could be. Definitely not 2.
p.s. was surprised to not find an online tool for calculating the area of boolean operations on 2D sets.

2025-08-19 06:14:01 UTC

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86 lines later Claude Sonnet 4 gave me S=2 which is clearly wrong.
I haven't worked out the right answer but it the area of a simple set operation on the rad=3/2 circles at the 4 corners and R. Something more like 1.6.

2025-08-01 11:38:59 UTC

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ok, seems odd at first glance. The Einstein universe is such a large 3-sphere that it is surely close to Minkowskian at the scales of hydrogen atoms.

2025-07-30 04:46:54 UTC

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presumably there is a cost to firing up immune cells otherwise your body would always have them present. So watching a movie of sick people has some cost on your body.
So is it good for you to watch medical movies? If you watch too many do you normalise and so become more vulnerable when a real sick person walks past?
Definitely something to think about, but the fact that are bodies do it isn't too surprising. We're always predicting things. We vomit when people all around us vomit, we yawn when people around us yawn.

2025-07-07 00:48:13 UTC

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I think there are two separate things here:
"there're essentially no black holes in the universe, only stars collapsing more and more slowly due to time dilation"
This does not appear to be Rovelli's view according to the paper above, as even the abstract talks about black hole formation. It is a view I have heard a few times and seems to be a general misunderstanding of GR.
"His proposal is that the singularity never forms because of the effects of quantum gravity and that these effects somehow spit out all the matter, creating a white hole."
This does seem to match with his paper.

2025-06-13 08:25:07 UTC

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makes sense to me, it is about standing waves around a point.

2025-05-31 23:11:57 UTC

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Personally I would say that the world's gravitational wave detectors are about the most important 'observatories' the world has, and I'm including the JWST and others in space.
The US spends more on defense than the next 9 countries combined. It should use that money to fund LIGO.

2025-05-14 08:35:32 UTC

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changing the search engine away from Google avoids the AI summary and has the added perk that I don't have to see Gulf of America (even in parentheses) on the search result maps.

2025-05-11 11:46:21 UTC

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There's a connection with Ford circles too. If you have one moon then you get gaps when the orbital period of the debris is a rational fraction of the moon's. Simpler fractions making larger gaps, so the base of the larger circles are the larger gaps.
So the thickest rings should be the periods hardest to approximate by a rational multiple of the moon's, such as phi. They're least resonant.
Orbital radius having a simple relationship with orbital period.

2025-05-04 04:46:23 UTC

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Scotland also has nice laws on the right to roam https://www.gov.scot/policies/landscape-and-outdoor-access/public-access-to-land/

2025-04-25 23:17:11 UTC

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Bananaman, "the muscles of 20 men and the mind of 20 muscles"
It's a funny parody of superheroes, he's missing a few marbles. His crow has most of the good ideas.

2025-04-22 05:50:04 UTC

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reminds me a bit of the Grey-Scott reaction diffusion systems: https://www.karlsims.com/rd-images.html

2025-03-06 01:58:46 UTC

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the thing is, people have been laughing at him since at least 2016. Remember the floating baby, the small hands, orange ape memes etc.

2025-03-06 01:05:14 UTC

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He's saying 'I dare you to fight back', of which there is only one effective response.

2025-01-10 02:22:54 UTC

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and let's rename Donald Trump to Donald Fart, it has a nice ring to it, and is the more up-to-date term.

2025-01-10 00:35:11 UTC

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definitely an interesting idea. Raises some questions.. why their nearest relative (Okapi) doesn't have it. Maybe because it is smaller.

2025-01-09 11:13:32 UTC

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Interesting. So arteries send blood to the dark area and veins take blood from the light areas of skin.
Maybe the idea is that - given you need varying contrast for camouflage - you want the blood to be at the coolest point before returning internally.
Hmm, doesn't sound right.
Maybe the blood helps to transfer the warm dark patch into the cool pale part, so evens out the overly hot dark patches.

2024-12-27 05:19:29 UTC

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the excitation time is indeterminate (much like the +c in an integral). So there is not one solution but an uncountable infinity of solutions, one for each excitation time in the positive Reals.
So it isn't probabilistic but a larger space of solutions.
If each solution had a Tony in it then each Tony would think that the ball had started rolling without cause at an arbitrary time.

2024-12-27 00:08:41 UTC

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Here's the Wikipedia summary: https://en.wikipedia.org/wiki/Norton%27s_dome
The problem is simpler with time reversed. You can construct a dome such that you can roll a ball up it and it comes to a halt at the top in finite time. This is perfectly believable to me, and is I'm sure a proven fact.
The problem is that information is lost, the historical state cannot be reconstructed from the stationary ball at the top.
There are similar problems in Newton's laws, but as far as I know they are all non-general (have measure 0 in state space) so require an infinitely precise setup. So they don't affect real-world predictions.

2024-11-27 05:13:18 UTC

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heh heh, mmm yes, I'll just get on that.

2024-11-27 05:02:06 UTC

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seems to me that this should be true of any fractal sponge.
And any fractal foam holds any general 2D surface (which can branch).

2024-11-18 04:22:46 UTC

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It's one of those 'Why do this rather than feed the starving?' sort of questions that could be asked about pretty much any profession or activity that we do.
Perhaps the answer has to do with diversity. Diversity of thought, diversity of interests etc. Also about balancing minimising bad outcomes vs maximising good outcomes. A pessimist minimises the bad, an optimist maximises the good. Maybe we can add that a realist understands a balance is good, but at the population level rather than individual level.

2024-11-01 00:27:49 UTC

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McDonalds just discovered them apparently. Also called spud bites by Pizza Hut and potato croquettes if we want to pretend they're fancy!

2024-10-31 23:07:42 UTC

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can do italics with \ (\textit{the text}\ )

2024-10-29 07:00:45 UTC

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may be interested in 2+2D spacetime story by @npub12cu…d38p

2024-10-22 03:44:59 UTC

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effectively the questions are wrong. Sad that nobody (or nobody nice) vetted the questions.
1. is probably around 'a' but it is not '*the* letter of this sentence'. It is the only isolated letter.
10. has no context on what 'the first word' is referring to.
11. If 0000 counts as a number then I guess it makes a little sense.

2024-10-04 11:17:22 UTC

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must be difficult to separate real effects from observer effects. Larger planets in shorter orbits presumably give stronger signals.
Maybe they're assuming observer bias is smooth on the graph, but maybe it isn't.