you can see a mostly-square shape of visited tiles developing around the origin

if our travel was euclidean, you would expect a circle, and if our travel was only vertical or horizontal (manhattan distance), you would expect a diamond

but since we have keys for moving diagonally at the same speed as horizontal or vertical, you would expect a square

however, you may have noticed the blocks in the heatmap don't look the same shape as an 80x25 terminal

that's due to the fact that terminal characters are typically around 2 time taller than they are wide

the 16x5 view accurately represents distances but it distorts how we think it should look

here's the same heatmap, but twice as tall to reflect character height

full size: http://i.imgur.com/SOYHSCS.png

this makes the tiles look the right shape to our eyes (like an 80x25 terminal), but as explained previously, this distorts distances in the sense of travel time

the original image better represents how remote the horizontally-distant tiles are

you could say this tall version better represents the total drawable area of ascii.town

this is the aspect ratio you would get if you screenshotted every single tile and stitched them into a single image

if you actually did stitch together screenshots of every tile into image, it would be very large!

my 80x25 cell terminal is 640x400 pixels, and there would be 512*512 screenshots

so, a raw RGB bitmap of the entire torus would be

640*400*512*512*3 = 201326592000 bytes = 187.5 GiB

#asciitown: it's bigger than you think!

on the other hand, PNG compression would make easy work of all the empty space

for example, the last heatmap image, http://i.imgur.com/SOYHSCS.png, as a raw RGB bitmap would have size

8192*5120*3 = 125829120 bytes = 120.0 MiB

but as a PNG it's only

172645 bytes = 168.60 KiB

hooray for PNG!