Thought I'd seen this earlier.

https://www.lexaloffle.com/bbs/?tid=27786

It's an unusual mathematical method - what's really odd is after he doodles for a-while, eventually he gets it in his head to take straight off up and right diagonally.

I hadn't studied the effect, but I'm pretty sure bolting out of there has got to be a mistake in the program or calculations, right ?

1) the mentioned program is my first pico-8 program, this one is the second :)
2) Langton's ant is a particular case of turmite, in this program you can choose from 43 different turmites, Langton's ant is #1
3) behavior you described is valid - https://en.wikipedia.org/wiki/Langton%27s_ant

This is kind of cool - do you have recommended reading on just the turmite? I am still not sure what I am seeing.

Could you add color as a 3rd dimension? Does that apply? I don't even know ... :)

Recommended reading:
https://en.wikipedia.org/wiki/Langton%27s_ant (here color extention is mentioned, maybe I'll write it too)
https://en.wikipedia.org/wiki/Turmite
https://en.wikipedia.org/wiki/Cellular_automaton

Gromozeka, how about this one which doesn't bolt out ? I'm curious to see the screen fill with this, without the "running away" behavior.

https://en.wikipedia.org/wiki/File:LangtonsAnt-nColor_RLR_13937.png

1) look at #32 and #33
2) I'll write color version too.

Trying ... Wow ! Got it. This is really curious. I wonder if random numbers are generated this way as you are only following a path and modifying the path based on what was plotted.

An interesting mathematical excursion, thanks, Gromozeka !

This is now one of my favorite carts. :D

Gromozeka, could you update to show what directions are being made when you change the turmite number ? If you like, I can make some tiles for you. Just display them at the top.

	[8x24]

You can copy and paste that directly in your tile area.

Display with: SPR(n,x,y)

Or if you want larger:

	[8x8]

Display with: SSPR() (see PICO-8 help for args)

Also maybe have an option for scale, so you can see an enlarged grid, also option for move one step at a time with keystroke so player can watch each individual move.

Thank you. I'll look at it later. Added support for multicolor turmites so far.

another update. now you can generate random multicolor turmites by pressing "Z".

Gromo, wouldn't it make more mathematical sense to just increase the color beneath the cursor by 1 until it flips over ?

That would be more interesting than a purely random color flipped to black and forth.

That's exactly what I'm doing. I'm not using random at all.
Look at #2,#3,#6 for example, you'll see that color patterns are not random.

Okay, it just looked like it for the initial ones. I'm a little unclear as to what the digits below represent ? If they are turning directions and moving ahead and stopping, could you please list what each digit represents ?

There are two extensions to Langton's ant that I implemented.

Here you can find description of multiple-colors one-state extension format (L and R) - https://en.wikipedia.org/wiki/Langton%27s_ant#Extension_to_multiple_colors

Here description of two-colors multiple-states extension format - https://en.wikipedia.org/wiki/Langton%27s_ant#/media/File:Turmite-121181121020-65932.png