I made a zoomable number line 🙂 https://vezwork.github.io/polylab/dist/demo/articles/exploring_spaces_3_and_a_half/

Now I want to see what you do with 2 dimensions. Like say for https://akkartik.itch.io/carousel/devlog/678890/new-version-after-51-days

Wow cool. I need to look at your stuff more @Kartik Agaram. I looked around a bit and thought your post about all 1d cellular automata on a canvas was especially cool. I made a 2D equation plotter with padding, zooming, and constraint nudging here: https://observablehq.com/d/67402a1c3d280238 I will have to add a zooming x and y axis to it!

This is great. Fun alternative: rather than showing decimal expansions, show fractions with all possible denominators up to a certain value, with that value increasing as you zoom in. (Like a https://en.wikipedia.org/wiki/Farey_sequence.) You might be able to see, e.g., how it’s particularly hard to find fractions near ϕ.

Oh beautiful @Joshua Horowitz. I thought about something like this while designing what numbers to show at each zoom level, line but didn't know it has a name! Farey sequence! I love the idea of visualizing that phi is hella irrational.

Hmm if you just want to show how real numbers are limits of sequences of rationals, you could do something like highlighting the ticks that represent truncations of pi as you zoom in. But maybe I don’t get what you’re saying yet.

This is overly complex because it is for the surreal numbers and too much of a manual illustration, but I'm thinking of something very roughly like this https://en.m.wikipedia.org/wiki/Surreal_number#/media/File%3ASurreal_number_tree.svg

this is sweet!! snap-to-smallest-visible-marker would be nice

Thanks @Arvind Thyagarajan! Good idea, I could add "press shift to snap" or something.

I wish I had more to say, but these are so cool! Keep up the great work!

I don’t get it yet (why is that branching off when it just fits into the original number line?) but you should go for it and show me.

A nice variant for numericists would be to show floating point numbers, whose density is high around zero and then decreases.

I was wondering too how this might help visualize the format for IEEE-754 floating point numbers.

The adventure game Heaven's Vault keeps a timeline of everything you do and learn in the game. It is about (space) archeology and uncovering the language of an ancient civilisation. You also uncover specific stories (a love-triangle murder etc) that happened over a few months, but 10,000yrs ago.

I'm curious what y'all think of this "slide rule from a parallel universe". Particularly from a standpoint of visual design. It consists of an optical sight for reading out data (the vertical red line in the center with a gap in the middle). Below the sight are queued up increasingly precise approximations of pi along number lines with increasing levels of zoom. As you pan downward, number lines above the sight adjust so that the value of pi in the sight is always in the center of the window. It's a little strange that approximations below the sight never move.

Why do the approximations below not move? I watched the video before I read the description and assumed the user was using arrow keys to adjust value (left/right) and adjust accuracy/scale (up/down)

Yeah I only use the y coordinate of the mouse. The constraint is the bubbles are always centered. The bubbles are approximations of pi on each line. As we go down, lines above adjust their approximations based on lines below. But yeah, an alternative would be to let the bubbles move left and right, and to always show the same number vertically centered in all lines.

These stacked number line explorations are cool @Kartik Agaram. I like the idea of "exploding" the zoom levels into stacked lines. It took me a little bit of time to get oriented with all the motion happening. its interesting to see each zoom level's vertically decreasing effect on the lines above it.