Is there a generic way to describe this emergent behaivor in the graphing of this program?

Ok so I made a simple program using turtle in python ,basicly its a turtle enclosed in a double loop;it moves foward a bit and then it moves right x where x is equal to 1,1,2,1,2,3,1,2,3,4,,etc for those who understand pseudocode its the following

for i from 1,2500:
   for x from 1,i:
      turtle.fw(1) //Or something smaller to zoom out

now it makes the following
enter image description here
pretty random just a lot of spirals, but if I zoom out by a factor of a hundred…
enter image description here
it makes a beautiful pattern, how does this patter emerge out of a random set of spirals? Also If you changeturtle.right(x) to turtle.right(x*80) it makes this:
enter image description here
still preaty random.. however if you zoom out by 10 this patern emerges:
enter image description here
Anyway I am not very expirienced in the subject of math however I think this could be quite interesting! I tried putting different x*n and most of the times it makes defined shapes I changed the code to javascript so if anyone wants to edit it and see what patterns emerge you can do that Here just edit y=71 to any number you wish, I have Checked that any repetitive 8’s make an incredible patern (8,88,888,etc) and that repetitive nines always make a straight line. If anyone has any idea why this patterns emerge or have any idea even what subject or sector of math invesigates 2d patterns from simple instructions It would be of great help!