r/3Blue1Brown

In a previous post I discussed the notion of a Collatz overlay built from 5 mod 8 and 0 mod 3 nodes. One refinement here is that there are nodes of in-degree 2 that are not 5 mod 8 (they are relatively rare - the exceptions I see are 1,23 mod 24)

This visualization allows you to see all 4, odd mod 8 nodes and in fact classifies them according to mod 24 too.

You give it a starting point with the ?a= parameter and then you can extend the graph is you like by clicking on a node.

This a fantastic way to develop an intuitive understanding of mod 8 and mod 24 Collatz dynamics.

https://wildducktheories.github.io/collatz/apps/collatz-graph/dist/?a=27

A fun game to play is greedily clicking on the red dots and then on 1,2 mod 3 nodes that result from such a clicking.

Does that game ever end? I think not.

Hi everyone,

I built H64LM, a research project to better understand modern LLMs by implementing one from scratch in PyTorch.

Instead of relying on high-level training frameworks, I implemented the core components myself attention, MoE routing, normalization, and the training loop.

Features

• 249M-parameter Transformer
• Grouped Query Attention (GQA)
• Sparse Mixture-of-Experts (8 experts, Top-2 routing) with 3 auxiliary routing losses
• SwiGLU, RoPE, RMSNorm
• Sliding-window attention
• Mixed-precision training, gradient accumulation
• Custom training loop (no Trainer abstractions)
• Checkpointing and resume support

The included checkpoint was trained on a subset of WikiText-103 to validate the pipeline end-to-end, not to be a strong model it's visibly overfit past epoch 10 (best val PPL ~40.5).

Known limitations are documented in the README, including batch-size-1-only generation and no true DDP (falls back to DataParallel).

GitHub: https://github.com/Haiderkhan64/H64LM

Feedback on the implementation or architecture is very welcome.

A visual, bite-sized mini-lesson for elementary school kids that bridges the gap between counting and algebra.

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Code available at https://github.com/zombimann/Mathematical-video-animations-and-visualization/blob/main/Kids_Elementary_Multiplication_Using_Circle_Grids.ipynb

You might also like https://np.reddit.com/r/3Blue1Brown/s/syRS2ZK39H

This visualizes the reduction of control systems block diagrams into their equivalent transfer functions.

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Code available at https://github.com/zombimann/Mathematical-video-animations-and-visualization/blob/main/Control_Systems_Block_Diagram_Simplification.ipynb

You might also like https://np.reddit.com/r/3Blue1Brown/s/hK6CRW5aLe

We previously posted separate 3D animations of QR decomposition by Gram–Schmidt, Givens rotations and Householder reflections.

Here is a 2D comparison of the same three geometric routes.

The goal is to show that all three methods reach the same kind of result, A = QR, but by very different geometric actions:

1. Gram–Schmidt: subtract projections and normalize
2. Givens rotations: rotate selected components to zero
3. Householder reflections: reflect vectors across chosen lines or planes

In 2D, the Givens case is almost trivial: only one rotation is needed to zero the lower-left entry. In higher dimensions, Givens QR proceeds by many such rotations, one entry at a time.

One detail worth noticing: Gram–Schmidt, in its standard form, produces positive diagonal entries in R. Givens and Householder versions may produce different signs depending on rotation/reflection sign choices. This is normal: QR is unique only after an extra sign convention is imposed, such as requiring positive diagonal entries in R.

More explanation and the 3D versions are here:
https://www.graphmath.com/la/visuals/qr/qr-three-geometric-routes.html

We will also add these 2D animations to that page.

We welcome feedback on clarity and presentation.

This video demonstrates a high-fidelity 2D simulation of the Magnus effect by modelling the trajectories of spinning spheres falling through a fluid medium.

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For code click https://github.com/zombimann/Mathematical-video-animations-and-visualization/blob/main/Bernoulli_Equations_Magnus_Effect.ipynb

You might also like https://np.reddit.com/r/3Blue1Brown/s/qxXGRIK2m2

A recursive algorithm, iterated as the curve winds through the entire volume of a cube.

Each step replicates the previous shape 8 times : order 5 already generates 32,767 connected segments, all from a single continuous line.

Full video : Generative 3D space-filling curve

We made three animated comparisons showing how eigenvectors and eigenvalues behave across different families of 2D linear transformations.

1. Non-symmetric matrices with real eigenvalues, where the eigenvector directions need not be perpendicular
2. Symmetric matrices with real eigenvalues, where the eigenvector directions are orthogonal
3. Real matrices with complex eigenvalues, where no nonzero real direction remains on the same line

In each animation, the transformation develops continuously from the identity matrix to the displayed matrix. The goal is to make the difference between these three cases visible rather than only algebraic.

Full-size animations and explanations:
https://www.graphmath.com/la/visuals/eigenvectors-eigenvalues-2d-transformations.html

As always, we welcome feedback on clarity and presentation.

The simulation focuses on the geometric nature of gravity, illustrating how mass distorts the fabric of spacetime and how accelerating masses generate ripples known as gravitational waves

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For code click https://github.com/zombimann/Mathematical-video-animations-and-visualization/blob/main/Gravitational_waves_3D_Space.ipynb

You might also like https://np.reddit.com/r/3Blue1Brown/s/jpzFVtaZrE

in radians, an angle is defined by θ =S/R). So if two circles have the same ratio. Do they really have same "angle"?

Or is it just mathematically same "angle"

For example

A circle s=1, r=1, θ=1 radian

B circle s=100, r=100, θ=1 radian

Mathematically they are indeed same "angle" but in real world they have very different physical separation.

A video animation of the drafting and rendering of a floor plan made using python. Link to code attached below.

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For code click Mathematical-video-animations-and-visualization/Programmatic_Floorplan_Generation_and_Animation.ipynb at main · zombimann/Mathematical-video-animations-and-visualization

You might also like https://np.reddit.com/r/3Blue1Brown/s/9hGCunVRUH

Newton's third law says the ball pulls Earth with exactly the same force Earth pulls the ball. So when you drop something, Earth genuinely accelerates upward to meet it — not a metaphor, an actual motion.

The reason nobody's ever felt it isn't that the force is smaller. It's identical. It's that acceleration is force divided by mass (a = F/m). The ball's tiny mass turns that shared force into ~9.8 m/s². Earth's mass turns the exact same force into about 10⁻²⁴ m/s² — real, just far too small to ever register.

Made a short trying to visualize that asymmetry with the two force vectors side by side. Curious if there's a cleaner way to show "same force, different consequence" than what I went with.

A while ago I posted my progress on Velyst, on rendering Typst in realtime game engine bevy. This time I want to show you something I made using it, combined with motiongfx, my motion graphics engine!

Link to YouTube (if u care to like & subscribe!): https://youtu.be/\_OGOaunoqMU?si=FdNhB16KqYBXJEqE

A bizarre linear system for neural networks applications:

https://archive.org/details/the-oddness-of-hd

One softwarez is:

https://archive.org/details/hd-dh-hd-dh-graph-viewer which we looked at before.

Another softwarez is: https://archive.org/details/h-12-d-dynamics

but that is for the atypical H₁₂ system, but you can still see the oscillations in some configurations. If you switch configurations you can see transitory oscillations as well. That is not due to dissipative effect, it is due to energy only slowly draining out of the old oscillation modes into the new one.

I keep getting banned on physics and neural network forums about this, where it might more properly be discussed. They really are incapable of absorbing information from "orthogonal" channels.

https://youtu.be/5HQFXxhDO7c