The Hidden Beauty of the Two Times Table.
This is the 2 times table wrapped round a circle, you can also see it in your cup of tea.
After reading @seafood 's great article the other day (found here) about a program he wrote to display numbers. I felt inspired to show some other interesting ways you can lay out numbers. This is one of my favorites and here's how it works.
Clock Arithmetic.
Making a pattern like this is actually quite simple, I started with a series of points spread round in a circle then started drawing straight lines between them doubling the number of the point so
- 1 goes to 2,
- 2 goes to 4,
- 3 goes to 6 and so on.
When you get to a number higher than the number of points then just like a clock you keep counting round.
Basically, the reason 15:00 hours is 3 o'clock is because we use what's called the Modulo operator. What happens is you divide 15 by 12 (the number of points) and use the remainder which is 3, the same rule applies here in the picture but I made a lot more than 12 points.
You really can see this shape in a cup of tea, maybe you already have, I hope after reading this seeing it will make you think of your two times table. :)
Weird Fractals.
The program isn't limited to just one multiplication table though and I made the number of points modifiable too so after a bit of playing following all the same rules here's the 72 times table mapped with 129,600 points.
Leave a comment.
If you have a favorite number and colour and you'd like a fractal making tell me and I'll post the results for you, if you're interested in the code that's cool too.
@pedrosgali
Upvoted and followed. Wow!
I love deep royal blue-purple mixes. And 12 is already my favorite number, but I like 88 too. :)
@voluntary led me here because he commented with this article link on a blog I just did:
I started my first episode of Eyes On The Minnows, where I feature Steemians that are still lesser known, and not bringing in much yet--Steemians that have quality to offer, that is.
You certainly do, so because of @voluntary, you're likely getting featured next week in my post to help bring community awareness to the small fish!
Here is the post I did featuring the first 10 for this week: https://steemit.com/steemit/@dragonanarchist/steemit-eyes-on-the-minnows-episode-1
Oh, can you do 13 and 62468 points?
Hey that would be great, thanks for the exposure. :)
I kinda changed the program to the point that it's hard to take stills now but check my next article and I'll do a GIF of 13 to 14 with all the steps in between.
EDIT: I made a few more changes and can now do both.
It is a very beautiful application of number theory, topology and geometry. These three fields perhaps are my personal three favourite streams of mathematics, the most fundamental, simple and very tightly interrelated. I am a visual thinker and these kinds of diagrams are representations of the network maps that appear in my mind when I think about numbers.
Thanks to @voluntary for pointing me to this post.
@pedrosgali I would be particularly interested to see a sequence of these number patterns for special number sequences also, Fibonacci, Primes, and so forth. The number 9 is particularly interesting, because its multiples also all sum to 9 due to the decimal system. By selecting clock patterns based on these multiples you can show other patterns as well. Part of what makes the pretty patterns in the middle is also to do with aliasing across the grid of pixels you are using, this acts as a moire type filter.
Hey @l0k1 Thanks for that great comment.
I was playing with this program last night and now use a different method for drawing the lines. Basically I got rid of the static points and now just calculate where the point would be which allows me to increment the points by an arbitrary value, in this case I'm trying 0.1 which shows the transition between 1 and 5 in 50 frames.
I'm going to try making some animations of this tonight for my next post but I'm currently having some trouble with the arbitrary number of points. It seems that over 50 or so points the patterns get too complex to show the progression to the next state so I may have to fiddle with that a bit more. Anyways, I hope you'll like it.
Just for you here's everyone's favorite transcendental, Pi to 10 decimals with 3041 points. :)
Ok, 24 and blue.
You didn't specify so I chose 35640 points, Hope you like it. :)
Could you make some animations with it? It might looks awesome.
Lol, that's exactly what I'm working on now. :)
Cool.
I wish I had more influence and my votes counted for more. This was a really nice little article and I'd never seen this stuff before.
Thanks man, looking forward to your follow up on the Primes.
I like this. I don't fully understand as my brain doesn't process maths too well but i like pretty patterns :) 13,purple, 488634 points.
oh, should it be a number in the 2x table? I don't think i've grasped this at all,lol. i'll go for 8 if so :)
No, any number is fine. Sorry for the late reply, I fell asleep. Here's 13 in purple with 488634 points. :)
Ooh it looks beautiful. Thank you! :)