# List of Lists with a specific goal **URL:** \ **Category:** Questions\ **Created:** [September 25, 2020, 8:05pm UTC](https://cl.desmos.com/t/list-of-lists-with-a-specific-goal/1572 "2020-09-25T20:05:49Z")\ **Posts on this page:** 13\ **Page:** 1
**Author:** ![HumanizedMath](https://yyz1.discourse-cdn.com/flex031/user_avatar/cl.desmos.com/humanizedmath/32/2947_2.png) [@HumanizedMath](https://cl.desmos.com/u/HumanizedMath)\ **Post date:** [September 25, 2020, 8:05pm UTC](https://cl.desmos.com/t/list-of-lists-with-a-specific-goal/1572/1 "2020-09-25T20:05:49Z")
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… ![image](https://canada1.discourse-cdn.com/flex031/uploads/desmos/original/2X/5/5e962e2d271eb8687270f2d5fe372008aaf53a88.jpeg) Thanks in advance. ---
**Author:** ![Daniel\_Grubbs](https://yyz1.discourse-cdn.com/flex031/user_avatar/cl.desmos.com/daniel_grubbs/32/719_2.png) [@Daniel\_Grubbs](https://cl.desmos.com/u/Daniel_Grubbs)\ **Post date:** [September 25, 2020, 10:44pm UTC](https://cl.desmos.com/t/list-of-lists-with-a-specific-goal/1572/2 "2020-09-25T22:44:08Z")
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). ```auto V1=(x1,y1) V2=(x2,y2) X=[x1, x1+(x2-x1)/n, ... x2] ``` ---
**Author:** ![HumanizedMath](https://yyz1.discourse-cdn.com/flex031/user_avatar/cl.desmos.com/humanizedmath/32/2947_2.png) [@HumanizedMath](https://cl.desmos.com/u/HumanizedMath)\ **Post date:** [September 25, 2020, 11:17pm UTC](https://cl.desmos.com/t/list-of-lists-with-a-specific-goal/1572/3 "2020-09-25T23:17:48Z")
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. ---
**Author:** ![HumanizedMath](https://yyz1.discourse-cdn.com/flex031/user_avatar/cl.desmos.com/humanizedmath/32/2947_2.png) [@HumanizedMath](https://cl.desmos.com/u/HumanizedMath)\ **Post date:** [September 26, 2020, 12:09am UTC](https://cl.desmos.com/t/list-of-lists-with-a-specific-goal/1572/4 "2020-09-26T00:09:42Z")
I just made a first attempt on my phone. > **[Regular Polygon Patterns](https://www.desmos.com/calculator/s9cwexkdwl)** Not sure how to get every iteration (“I”) to show…thinking maybe need another sum ---
**Author:** ![HumanizedMath](https://yyz1.discourse-cdn.com/flex031/user_avatar/cl.desmos.com/humanizedmath/32/2947_2.png) [@HumanizedMath](https://cl.desmos.com/u/HumanizedMath)\ **Post date:** [September 26, 2020, 1:01am UTC](https://cl.desmos.com/t/list-of-lists-with-a-specific-goal/1572/5 "2020-09-26T01:01:32Z")
Well I think I’ll be able to get to it eventually. Hard writing this out on my phone… Got the outlines > **[Regular Polygon Patterns](https://www.desmos.com/calculator/ke6qxyettk)** ---
**Author:** ![JayChow](https://yyz1.discourse-cdn.com/flex031/user_avatar/cl.desmos.com/jaychow/32/1674_2.png) [@JayChow](https://cl.desmos.com/u/JayChow)\ **Post date:** [September 26, 2020, 2:11am UTC](https://cl.desmos.com/t/list-of-lists-with-a-specific-goal/1572/6 "2020-09-26T02:11:44Z")
Its a little (or a lot) clunky but I think this does what you want? > **[Desmos | Graphing Calculator](https://www.desmos.com/calculator/jnp6rx6svr)** ---
**Author:** ![HumanizedMath](https://yyz1.discourse-cdn.com/flex031/user_avatar/cl.desmos.com/humanizedmath/32/2947_2.png) [@HumanizedMath](https://cl.desmos.com/u/HumanizedMath)\ **Post date:** [September 26, 2020, 4:44am UTC](https://cl.desmos.com/t/list-of-lists-with-a-specific-goal/1572/7 "2020-09-26T04:44:00Z")
It does. But I am still stubbornly struggling on my own trying to make sense of how to get the points in between. ---
**Author:** ![JayChow](https://yyz1.discourse-cdn.com/flex031/user_avatar/cl.desmos.com/jaychow/32/1674_2.png) [@JayChow](https://cl.desmos.com/u/JayChow)\ **Post date:** [September 26, 2020, 5:04am UTC](https://cl.desmos.com/t/list-of-lists-with-a-specific-goal/1572/8 "2020-09-26T05:04:12Z")
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 ---
**Author:** ![HumanizedMath](https://yyz1.discourse-cdn.com/flex031/user_avatar/cl.desmos.com/humanizedmath/32/2947_2.png) [@HumanizedMath](https://cl.desmos.com/u/HumanizedMath)\ **Post date:** [September 26, 2020, 5:08am UTC](https://cl.desmos.com/t/list-of-lists-with-a-specific-goal/1572/9 "2020-09-26T05:08:21Z")
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. ---
**Author:** ![HumanizedMath](https://yyz1.discourse-cdn.com/flex031/user_avatar/cl.desmos.com/humanizedmath/32/2947_2.png) [@HumanizedMath](https://cl.desmos.com/u/HumanizedMath)\ **Post date:** [September 26, 2020, 2:39pm UTC](https://cl.desmos.com/t/list-of-lists-with-a-specific-goal/1572/11 "2020-09-26T14:39:15Z")
Figured it out…never lost faith…definitely lost sleep > **[Regular Polygon Patterns](https://www.desmos.com/calculator/vrsbpxp6hm)** ---
**Author:** ![HumanizedMath](https://yyz1.discourse-cdn.com/flex031/user_avatar/cl.desmos.com/humanizedmath/32/2947_2.png) [@HumanizedMath](https://cl.desmos.com/u/HumanizedMath)\ **Post date:** [September 27, 2020, 4:02am UTC](https://cl.desmos.com/t/list-of-lists-with-a-specific-goal/1572/12 "2020-09-27T04:02:53Z")
Cracked it out. > **[Regular Polygon Patterns](https://www.desmos.com/calculator/grsgxg8u4z)** ![image](https://canada1.discourse-cdn.com/flex031/uploads/desmos/original/2X/a/a73b28b186f70a4fc6667487fa4ee487535987fa.png) ---
**Author:** ![Thomas\_Garrison](https://yyz1.discourse-cdn.com/flex031/user_avatar/cl.desmos.com/thomas_garrison/32/3579_2.png) [@Thomas\_Garrison](https://cl.desmos.com/u/Thomas_Garrison)\ **Post date:** [May 3, 2022, 4:50am UTC](https://cl.desmos.com/t/list-of-lists-with-a-specific-goal/1572/13 "2022-05-03T04:50:49Z")
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: > **[Regular Polygon Patterns](https://www.desmos.com/calculator/f0r0uxsdmv)** > > Regular Polygon Patterns 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 ---
**Author:** ![Argitechno](https://yyz1.discourse-cdn.com/flex031/user_avatar/cl.desmos.com/argitechno/32/4586_2.png) [@Argitechno](https://cl.desmos.com/u/Argitechno)\ **Post date:** [October 25, 2023, 1:49am UTC](https://cl.desmos.com/t/list-of-lists-with-a-specific-goal/1572/14 "2023-10-25T01:49:36Z")
Here’s a way to do it in one line, using iteration, more iteration, and list sums. Lots of lists. > **[Regular Polygon Patterns](https://www.desmos.com/calculator/hklvyxzh2x)** > > Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. P.S. I know its been a year and a half but this was fun to solve in a new way and somebody could use the information.