This blog is about Simon, a young gifted mathematician and programmer, who had to move from Amsterdam to Antwerp to be able to study at the level that fits his talent, i.e. homeschool. Visit https://simontiger.com

Simon had his first public performance in front of a large audience last Saturday (February 9, 2019): he spoke about his Times Tables Visualization project at the Processing Community Day in Amsterdam!

Simon writes: You can access the code of the poster and the animation (and the logo for my upcoming company!) and download the presentation in PowerPoint, on GitHub athttps://github.com/simon-tiger/times_tables

If you’d like to buy a printed copy of the poster, please contact me and I’ll send you one. Status: 3 LEFT.

Simon getting ready for his presentation at the Processing Community Day Amsterdam, printing additional copies of his ginormous Times Tables Visualization poster at the Antwerp Art Academy (made possible thanks to our wonderful friend, photographer Oxiea Villamonte). If you’re into creative coding and math, please come to the event (Simon will be speaking around 15 p.m.) There will be a limited number of Times Tables Visualization posters available for sale!

My Times Tables Visualization Poster has arrived! Will probably present this at @CC_Amsterdam @ProcessingOrg Community Day Amsterdam! https://t.co/ChTg0eOLIn

Simon has made an enormous poster from his earlier animated version of the Times Tables Visualization! Simon is hoping to present this project at the Processing Community Day in Amsterdam in January 2019. The poster is already being printed!

Simon writes: This is a visualization for the times tables from 1 to 200.
Start with a circle with 200 points. Label the points from 0-199, then from 200-399, then from 400-599, and so on (you’re labeling the same point several times).

We’ll first do the 2x table. 2×1=2, so we connect 1 to 2. 2×2=4, so we connect 2 to 4, and so on.

2×100=200, where’s the 200? It goes in a circle so 200 is where the 0 is, and now you can keep going. Now you could keep going beyond 199, but actually, you’re going to get the same lines you already had!

For the code in Processing, I mapped the two numbers I wanted to connect up (call them i), which are in between 0 and 200, to a range between 0 and 2π. That gave me a fixed radius (I used 75px) and an angle (call it θ). Then I converted those to x and y by multiplying the radius by cos(θ) for x, and the radius by sin(θ) for y. That gave me a coordinate for each point (and even in between points, so you can do the in between times tables as well!) Then I connect up those coordinates with a line. Now I just do this over and over again, until all points are connected to something.

Unfortunately, Processing can only create and draw on a window that is smaller than a screen. So instead of programming a single 2000px x 4000px poster, I programmed 8 1000px x 1000px pieces. Then I just spliced them together.

Simon shows his Times Tables Visualization in Processing (Java) and talks about how it’s connected to Mandelbrot Set. See the code with the README on GitHub: https://github.com/simon-tiger/times_tables

View the full animation here:

Simon writes: This is a visualization for the times tables from 1 to 200 (including the in-between numbers that are multiples of .01). I used modular arithmetic to write the code:

0. Start with a circle with 200 points (I’ve chosen 200, your number could be anything, but we’ll use 200 in the instructions).

1. Label the points from 0-199, then from 200-399, then from 400-599, and so on (you’re labeling the same point several times).

2. We’ll first do the 2x table. 2×0=0, same thing so we don’t do anything. 2×1=2, so we connect 1 to 2. 2×2=4, so we connect 2 to 4, and so on.

3. 2×100=200, where’s the 200? It goes in a circle so 200 is where the 0 is, and now you can keep going.

4. Now you could keep going beyond 199, but actually, you’re going to get the same lines you already had!

5. You can now create separate images for the 2x table (which we’ve just done), the 3x table, the 4x table, the 5x table, and so on. You can even try in-between numbers (like 2.53) if you want.

In the program, you see an animated image at the left of the screen, and 4 static images (representing examples of times tables) to the right of that. They represent the 2x, 34x, 51x and 99x tables.

The idea of a times tables visualization comes from a video by Mathologer, but the code Simon wrote completely on his own.