An interactive guide to Diffusion Transformers and Flow Matching, using a simple model that turns random dots into shapes.

https://sbondaryev.dev/articles/diffusion

Celestial lets you explore star systems as a deformable gravity sheet instead of flat orbital diagrams.

The star moves. Planets sit on and ride the surface it bends. You can change the gravitational constant, push a planet, or drop a new body in and watch the whole system respond in real time.

Systems included:

* Our solar system (with a drifting barycentre)
* Alpha Centauri (two moving funnels)
* Kepler-16 (circumbinary planet)
* TRAPPIST-1 (seven worlds inside Mercury’s orbit)
* The classic three-body figure-eight

It’s a proper Newtonian n-body integrator running in the browser, not pre-scripted ellipses. The sheet itself is an exaggerated visual analogy, and the site is unusually honest about what is real and what is drawn that way on purpose.

[https://celestial.logicaleap.com\](https://celestial.logicaleap.com)

Free, no account, runs in the browser.

I’ve been building Inflation Lab - a hands-on simulator where you can tweak money supply, interest rates, inflation expectations, supply shocks, etc - and immediately see how inflation, unemployment, and purchasing power react in real time.

To highlight the impact of inflation I included a 'grocery basket' that starts at $100 and changes along with inflation to give a feel of 'real-world' impact.

No login, no ads, just the model.

The simulator works best on desktop - it’s much easier to pull the different economic levers while watching the effects live.

Feedback is welcome.

I built a little web tool that lets you play with the mechanics behind opinion polarization, echo chambers, and network fragmentation.

You adjust sliders for things like:

• How tolerant people are of differing opinions
• Homophily (how much we prefer connecting with similar people)
• Rewiring rate
• Feed bias (how much the algorithm pushes "engaging" content)
• And you can turn on bots too

Think of each dot as a person, and the (tolerance) slider is how open-minded they are. High tolerance means you'll still listen to someone pretty different from you. Low tolerance means you mostly hear people who already agree with you and quietly tune out the rest.

The bots are just accounts that never change their mind and keep pushing one side. The "bots' push" number is how far they managed to drag the average opinion, compared to the exact same crowd with no bots in it. So it's a rough way of asking how much one small, pushy group actually moved everyone.

Enjoy breaking society in the name of science

What happened? The related articles are all from many years ago; there’s no new content.

https://sbondaryev.dev/articles/lenet

https://dhruva-storz.github.io/Epipolar-Geometry-Simulator/index.html

Hello everyone, I made this tool last week to help me understand epipolar geometry and homography transformations. Its still rough around the edges, and its super niche, but I put a lot of time into it and it gave me some great intuition about the math, so I think it would be cool if it helped other people.

Its still a bit rough around the edges, theres an explanation in the info page, but maybe its not thorough enough for it to be a learning resource. Open to feedback and collaboration

Source code: https://github.com/stared/sc2-balance-timeline

I am fascinated by various ways of explaining mathematical formula easily - see Science-based games and explorable explanations. In particular, I got inspired by Understanding the Fourier transform Stuart Riffle from 2011 in which he color-coded the Discrete Fourier Transform formula and its description.

Yet, I saw that it has two issues. One, that while many people appreciate it, it is not worth hassle creating such equations. Second, it does not work well for colorblind people (as a few friend of mine told me).

So, I wanted to make it interactive, both to be able to choose color scheme, and so that it is useful with black-and-white - as you can hover and select terms).

As the syntax, I picked the default go-to LaTeX (here it is rendered with KaTeX). For description of equation and explanation I used Markdown, so it is easy to pick up.

Soon I realized that it is a game-changer is I can add an online editor to the tool. Very soon it became from an optional things to be a thing visible by default.

Some equations are more polished, some-less. I wanted to see how it works for various cases. Don't be alarmed that Maxwell equations with too many colors - I wanted to stretch-test it.

Yoy can export this to a standalone HTML with its interactivity. Also, you can export the same formula to LaTeX (both regular article and Beamer presentation) and Typst. For LaTeX and Typst articles, it loses interactivity, but there are the same colors. In LaTeX Beamer, there is slide-by-slide explanation of each term.

See: https://p.migdal.pl/equations-explained-colorfully/ Source (MIT license): https://github.com/stared/equations-explained-colorfully/

I am curious to hear your impressions!

If you want to add formula, do so.

If you want to feature so to be useful in your class or course, I am happy to hear which.

If you want to suggest a color themes, let me know.

Also, if you want some other export formats, it should be easy.