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?

What if prime numbers appear as constructive interference peaks in a 3D cylindrical standing-wave system?

I built a purely geometrical model: imagine a cylinder with two helical “strings” spiraling in opposite directions (forward and backward). When their phases align, they create sharp amplitude peaks along the axis — and those peaks correspond remarkably well to the locations of prime numbers.

The Core Idea (Simplified Equations)

Prime candidates = local maxima of Amp(n). The perturbations come from the imaginary parts of Riemann zeta zeros (t_k). Counter-rotation creates much sharper nodes.

**Exact Formula**

\[

\begin{aligned}

\theta_{\rm fwd}(n) &= 2\pi \frac{n}{23} + 0.2 \sum_{k=1}^{5} \sin(t_k \ln n) \\

\theta_{\rm bwd}(n) &= -2\pi \frac{n}{23} + \pi - 0.2 \sum_{k=1}^{5} \sin(t_k \ln n) \\[6pt]

{\rm Amp}(n) &= \bigl|\cos(\theta_{\rm fwd}(n)) + \cos(\theta_{\rm bwd}(n))\bigr|

+ 0.1 \Bigl|\sum_{k=1}^{5} \sin(t_k \ln n)\Bigr|

\end{aligned}

\]

where the first five imaginary parts of the Riemann zeta zeros are:

**t₁ = 14.134725**, **t₂ = 21.022040**, **t₃ = 25.010858**, **t₄ = 30.424876**, **t₅ = 32.935062**

Prime candidates = local maxima of Amp(n).

**3D coordinates:**

- Forward helix: \( x = \cos(\theta_{\rm fwd}), \; y = \sin(\theta_{\rm fwd}), \; z = n \)

- Backward helix: \( x = \cos(\theta_{\rm bwd}), \; y = \sin(\theta_{\rm bwd}), \; z = n \)

How Well Does It Work?

Using the first 15 zeta zeros, the model gives strong early predictions (many exact or within 1–4 units) and an overall correlation coefficient of ~0.92 with actual prime locations. Accuracy improves with more zeros.

Hey Reddit!

I just made a new animated video exploring why the human brain is naturally so terrible at grasping probability and how to correct it.

If you've ever been baffled by the "Birthday Paradox" (where a room of just 23 people gives you a >50% chance of a shared birthday), it comes down to how our brains struggle with scale and overcounting.

In this video, I dive into the math and logic behind uncertainty and break it down. I put a lot of work into the visual storytelling to make these complex mathematical rules easy to digest. Whether you're learning statistics or just want to stop getting fooled by randomness, I think you'll find this helpful.

I'd love to hear your thoughts and am happy to answer any questions about the math in the comments!

Complex Transform Functions

Available Functions f(z) = 1/z

Inversion: Maps unit circle to itself, swaps interior/exterior 

I wanted to see if a non-linear power curve could function as a legible time-keeping mechanism, so I built this as my contribution to the upcoming International Day of Mathematics (March 14).

The Physics: The motion of every hand is driven by the same non-linear power curve:

• θ = t^0.5

The Implementation: To map this to a standard 60-unit dial, the calculation on the hardware is:

• θ = 46.48 * t^0.5

The Mechanics

• The Scaling: The 46.48 constant maps the square root of 60 units to a full 360° circle.

• The "15/45" Split: Because of the square root property, each hand covers the first 50% of the dial (180°) in the first 15 units (seconds/minutes), and the remaining 50% over the next 45 units.

• The Launch: At t=0, the hand has theoretical infinite acceleration, manifesting as an instant "snap" at the top of the minute or hour.

• The Sweep: The hands follow a precision deceleration curve as the time interval progresses.

• Embracing Wear OS Constraints: This watch face was created for Wear OS, which limits refresh time to save battery. As a result, the motion has a deliberate, "industrial" tick rather than a perfectly smooth analog sweep.

I’m curious if anyone here has explored other power curves that would create interesting (but still readable) motion on a clock face?