# List of Lists with a specific goal

I have asked this question before and I have (fuzzily) learned a work around or two. I am trying to build a geometric pattern using points. I am wondering what ideas the collective brain trust here could offer… I would like a slider that would show iterations of the following object…

Well, vertices are fairly simple dilations of n=1.
Once you have vertices, something like this for all the points on a side? May need an absolute value. Obviously something similar for Y, then (X,Y).

``````V1=(x1,y1)
V2=(x2,y2)
X=[x1, x1+(x2-x1)/n, ... x2]
``````

Yeah partitioning the line segments will definitely take care of those between the points. I’m struggling with nesting the lists properly. Haven’t quite wrapped my head around the interior ones of the previous iteration, I think I could get the expansion of the outer edge going though using polar coordinates. Using just 5 lists.

That is n=4 would show all of the dots, not just the orange ring.

I just made a first attempt on my phone.

Not sure how to get every iteration (“I”) to show…thinking maybe need another sum

Well I think I’ll be able to get to it eventually. Hard writing this out on my phone… Got the outlines

Its a little (or a lot) clunky but I think this does what you want?

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It does. But I am still stubbornly struggling on my own trying to make sense of how to get the points in between.

Fun! We still do really do recursive functions which make it a little tough. If you get stuck trying to make it endless, reducing to a reasonable number of iterations might make it clearer. @aknauft might have some fun ideas for you as well

I’m banging my head against the wall trying to generate this list:
L1=0,1,2,3,4,0,0,1,1,2,2,3,3,4,4…

Messing around with mod and some other things. Got close a few times… Basically, trying to do what you had but generalized for any regular polygon. Kind of figured out the flow of points it will need to follow.

Figured it out…never lost faith…definitely lost sleep

Cracked it out.

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Here’s a super easy way to do it, just using a list to get all the iterations to show at once. I got around the “lists in lists” by using for statements and doing x and y separately:

P.S. I know its been two years but this was fun to solve, and I felt like someone could use this information even farther into the future