Christian Lawson-Perfect @christianp@mathstodon.xyz

this is cool: A mix of experiment and explorative explanations, embedded in the context of #replicationCrisis and a sprinkle of robust statistics / outlier.

How random are you?

https://pudding.cool/2022/04/random/

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For a \(n\times n\) grid, the lights out game can be considered as solving a linear system over \(n^2\) variables in mod \(2\). It takes \(O(n^6)\) time. Surprisingly, there is a \(O(n^3)\) time algorithm. https://chaoxuprime.com/posts/2019-01-12-lights-out-game.html

Thank god

@christianp That sounds like a beeometric sequence to be. Its sum would be \( \frac{1}{1-b} \).

Still obsessed about how Nintendo made Abstract Algebra the video game and I'm just now playing it. Each battle takes an optimal configuration of enemies, applies the composition of two allowed permutations (ring/diameter cycles), and presents results to the player. Apply the right inverses in the right order and you'll one hit KO everyone before they can strike back.

If you're into chaos, you might enjoy this visualization of the standard map
\begin{align}
p_{n+1} = p_n + K \sin \theta_n, \\
\theta_{n+1} = \theta_n + p_{n+1},
\end{align}
with varying \(K\). It's pretty hypnotic https://www.shadertoy.com/view/WdjcW3

People from Mathstodon: if you want to share your maths with people from other instances, keep in mind that LaTeX rendering is only available on a browser, and for people also on mathstodon.

If you still want to write formulas, mathstodon can be used to export LaTeX to unicode, like \sum to ∑, \prod to ∏, and so on.

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Example: ϕ(x)=∑ₖⁿ xᵏ

It's not perfect, but you can see it on a phone app!

Rep-tile experiment with holes - three parallelograms makes a triangle, 8 triangles makes a parallelogram. It's more like a second order rep, not sure what to call this. #mathart #fractal #tiling

I love questions like this