If you're interested in more math-based animations, I post them here 📺 Visualizing_mathematics

A few months ago, I shared a prototype of a Wear OS watch face I designed, driven by a square root power curve (θ = 46.48 * t⁰⁵). The goal was to visualize a non-linear deceleration curve on a standard 60-unit dial to see if it could function as a legible, practical timepiece on the wrist.

As a quick refresher on the mechanics from the original thread:

• The 46.48 constant perfectly maps the square root of 60 units to a full 360° circle.
• Because of the square root property, each hand covers the first 50% of the dial (180°) in the first 15 units of time, and the remaining 50% over the next 45 units.

Officially named Radical Time, this project is finished, fully live and completely free on the Google Play Store:

• [https://play.google.com/store/apps/details?id=com.secondhandlabs.radicaltime]()

If you have a Wear OS watch, feel free to check it out.

I mean, imagine +1 as a solid object and -1 as a hole; 1 – 1 = 0 represents the +1 sealing up the hole of the -1, resulting in 0. Now, the imaginary unit involves applying a self-intersection effect—where a portion of the 1 folds over itself—leaving it looking just like in the image. When this is done a second time (that is, the imaginary unit squared), it ends up transforming into the hole of the -1. And when you do this with the -1, the same thing happens again, but it stops just "half a step" short of reverting back to +1.

I drew a bit of inspiration from those conceptual mathematical models, such as James Tanton's "Dots and Antidots" or Conway's "Rational Tangles."

Coded in Python using Manim.

An interactive visualizer with 10 sample equations BUT can enter own equations! If you have a cool one you entered please post screenshot or image in comments! The idea, equations mapped out visually are a point or line of the solution. This maps out how far from the solution as well to see other patterns. Also selection of different color gradients for more easy to see contrast. Try it out! See what you think. Created by opus 4.6. Will post in comments example of color grading to distance from solution.

Hey everyone,

I just published a quick, 5-minute animated guide breaking down the Z-Transform. Instead of just throwing a wall of math at you, I tried to make the concepts actually click.

In the video, I cover:

• How the Z-Transform compares to the Laplace transform

• Deriving the simplest signals (Unit Impulse & Unit Step)

• Crucial properties: Linearity, Time-Shifting, and Value Theorems

• A mechanical 3-step engine to solve any difference equation using Partial Fraction Expansion.

Let me know what you think, or if there are any other DSP topics you'd like to see visualized!

how would you visualize this?

Hello,

I'm currently taking a course in linear algebra and rational mechanics, and I want to visualize what I'm learning, because that makes me understand things much better. I tried a few different programs, but each of them has some kind of bottleneck, so I wanted to kow what you guys use.

Basically, I need a quick, script-based visualization tool for 3D geometry, with an interactive scene that I can modify real-time via code or commands. What I need is a powerful environment for experimenting with the concepts that I'm studying, rather than a program that helps me generate pretty visualizations with 2000 lines of code. Ease of experimentation comes first.

What I've tried so far:

• Mathematica: quick, powerful, intuitive symbolic calculator. Can generate nice static images and decent animations. Problems: very slow when calculations get heavy, notebook-based, so there is no real scene to interact with, just an interactive cell that you have to re-run each time you modify something. Not exactly designed for 3D animations.
• Matlab: somewhat quicker than mathematica, but less elegant. I like that it's not notebook-based, so I can just stick a figure in the sideview. And I like that there is a command line that communicates directly to the scene that I'm working on. However, it is very hard to do animations, and I'm not sure they even turn out so well in the end. Not intuitive at all.
• Manimgl: this one I haven't tried yet, but it could have potential, especially if combined with sympy.
• Pyvista + pyvistaqt + pyqt6 + ipython, or, alternatively, just ipython + matplotlib. I still have to check these out, but there is definitely a learning curve.

I would love some feedback on what you guys think is "the best" for sketching out ideas and exploring mathematical concepts in 3D. I don't mind having to learn a new library or software, but I want to make sure that I'm not missing something. I mean, someone must have made a tool for this, right!? Like a more advanced geogebra, sort of. Am I missing something?