I made things a bit more interesting: Random obstacles, which cause life forms to survive in niche area's

Javascript demo: https://westy31.home.xs4all.nl/ScrapBook/GwJS_EatCells.html …

Oh my goodness I've just learned a thing about The Matrix that causes it to make a lot more sense: In the original script the humans were used as neural network compute clusters by the Machines and as a crucial component of The Matrix itself.

Which is why humans who were aware of the simulation could control aspects of The Matrix - their minds were part of its foundation.

Unfortunately the test audiences had trouble understanding this concept so the studio changed the human role to "batteries".

Here is an old animation I got from the Scientific American years ago. Make a torus with NxN squares, with P different cell types. Type 1 eats type 0, type 2 eats type1, ….type 0 eats type (P-1). Start with random values, and itereate!

Just as you think one cells starts to ‘win’, a ‘deadly spiral emerges that kills all other life.

It's still \(\pi\)-day here (barely). My favorite of today's \(\pi\)-day videos is Vi Hart's, https://www.youtube.com/watch?v=imfqczglelI — kind of conveys what I feel about the significance of random concatenations of digits.

@andrewt's Aperiodical piece on average numbers of representations as sums of squares (https://aperiodical.com/2019/03/buzz-in-when-you-think-you-know-the-answer/) is good too.

I just found out David Metzler exists, here's his very gentle 47 part intro into differential forms:

https://www.youtube.com/watch?v=M5wrnwlm8lw

Or this cool series, about the Hodge connjecture:

Fitting In

Stereographic projection of putatively optimal packing of 124 points on the unit sphere.

Source code and explanation: https://community.wolfram.com/groups/-/m/t/1579272

Doing a relativity project, I came accros a talk by Einstein, in which he argues for not rejecting ether theory!

https://en.wikisource.org/wiki/Ether_and_the_Theory_of_Relativity

He says that although special relativity suggests that the ether is a redundant concept, in general relativity it might be usefull, since space-time, according the general relativity, has local physical properties.

Following up on my previous post on Newton’s theorem that you can have circular orbits that pass infinitely fast through the origin, if and only if the gravity law were r^-5.

I did an animation with more frames, but fewer graphics.

Amazing, that Newton figured this out around 1680! Newton had to first invent calculus himself, and come up with the revolutionary new way of looking at the physical world using mathematics.

Newton is of course famous for discovering the inverse square law of gravity. But he also found a number of interesting theorems about central force fields. One of them is illustrated here: If the force law is 1/r^5, then there are solutions that are circles which pass through centre! The velocity is infinite as the ‘planet’ shoots through the central ‘black hole.

Wikipedia on central force theorems:

https://en.wikipedia.org/wiki/Classical_central-force_problem

@GerardWestendorp And a million dollar rich.

[PART3]

Next, you slightly decrease or increase the guess of the variable, depending on the error.

If you do this gently enough it I thought it might be fun to try this with a Sudoku puzzle. For each non-given cell, I demand the difference between any other cell in the same row, column or sub-square is greater than 1 and less than -1, If not, I slightly change the variable away from the other number. (Working modulo 9, so 1 is next to 9).

[PART2]

Next, you slightly decrease or increase the guess of the variable, depending on the error.

If you do this gently enough it will converge to a minimum error. This will produce a local optimum: you cannot decrease the error by slightly wobbling any of the variable. In physics this is often the solution you want.

*Relaxation versus NP*

In engineering, many problems, mechanical, thermal, fluid dynamics, electro magnetic, can be solved by a relaxation method. First you guess all variables, for example by a random number. Then for each variable, you compute the error: You take all equations that the variable should satisfy, and sum over the errors. You take care that for each equation the derivative of the error to your variable is positive.

[PART1]

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Visualisation projects of mathematics and physics.

Joined Oct 2018