### Author:  [@Loumen\_Cai](https://cl.desmos.com/u/Loumen_Cai)
#### Post date: [October 3, 2025, 4:00am UTC](https://cl.desmos.com/t/creating-lists-of-4d-points/8272/1 "2025-10-03T04:00:46Z")
I am trying to create a full 4D quaternion-based mandelbulb in desmos using definitions from .desmos.com/calculator/5aok5agmrf (I couldn’t find the original quaternion one so I settled for an octonian link by someone else). I have currently implemented it for evaluating singular points, but I can’t figure out how to make some sort of list of coordinates that 1. creates a “grid“ of 4D points and 2. works in desmos but I can also call specific parts from the list such as real, i, j, k. Desmos doesn’t support 4D points obviously and I can’t get it to work just using (X, Y)forX=, Y=, Z=, W= because there are duplicates (I was assuming each coordinate (x1, y1), (x2, y2) would count as 1 4D coordinate, so real would be L.x[1, 3, 5,…], i would be L.y[1, 3, 5,…] j would be L.x[2, 4, 6,…] ect…). After that, it should work, just testing for f(iterations)\<2 at each 4D point.
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### Author:  [@Guzman\_Tierno](https://cl.desmos.com/u/Guzman_Tierno)
#### Post date: [October 3, 2025, 6:21am UTC](https://cl.desmos.com/t/creating-lists-of-4d-points/8272/2 "2025-10-03T06:21:26Z")
That’s really interesting.
I’m not sure I understand your issues.
Obviously Desmos doesn’t support quaternions natively, so we have to define the operations and then we have to use a projection into the 3D space to show them.
Can you share your code?
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### Author:  [@Loumen\_Cai](https://cl.desmos.com/u/Loumen_Cai)
#### Post date: [October 3, 2025, 3:47pm UTC](https://cl.desmos.com/t/creating-lists-of-4d-points/8272/3 "2025-10-03T15:47:15Z")
P.S. Even though I can’t get a real list of 4D points I need some sort of method to reliably do so, which is currently a+bi+cj+dk≡(a, b), (c, d)
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### Author:  [@Loumen\_Cai](https://cl.desmos.com/u/Loumen_Cai)
#### Post date: [October 3, 2025, 3:47pm UTC](https://cl.desmos.com/t/creating-lists-of-4d-points/8272/4 "2025-10-03T15:47:18Z")
Currently I have been using a system where its A\_{0}=\left(X,\ Y\right)\operatorname{for}X=a\_{0},\ Y=a\_{0}, B=\left(X,\ Y\right)\operatorname{for}X=A\_{0}.x,\ Y=A\_{0}.x, a\_{0}=\left[-1,…1\right], however testing for unique(B) says that there are tons of repeats (unique(B)\
### Author:  [@Guzman\_Tierno](https://cl.desmos.com/u/Guzman_Tierno)
#### Post date: [October 3, 2025, 6:06pm UTC](https://cl.desmos.com/t/creating-lists-of-4d-points/8272/5 "2025-10-03T18:06:22Z")
So, I’m not familiar with Mandelbrot in 3D (Mandelbulb) using quaternions …
I’m trying to understand how it works.
In doing so I tried to simplify the code a bit and I think I found some bugs:
[https://www.desmos.com/calculator/bypppbrprf](https://www.desmos.com/calculator/bypppbrprf)
for example if you consider the definition of M\_a
the last factor cannot be
y\_1[3 length(A)/4 … 4 length(A)/4+1]
because 4 length(A)/4+1 = length(A)+1 and this is out of the bounds of the array.
I think it should be y\_1[3 length(A)/4 … 4 length(A)/4].
So, I get that we do something similar to Mandelbrot in 2D …
but I don’t understand when you say that the problem is the 4D grid.
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### Author:  [@Loumen\_Cai](https://cl.desmos.com/u/Loumen_Cai)
#### Post date: [October 4, 2025, 5:14pm UTC](https://cl.desmos.com/t/creating-lists-of-4d-points/8272/6 "2025-10-04T17:14:10Z")
What I was doing was defining a+bi+cj+dk as (a, b), (c, d). I could find a reliable way to generate all possible combinations of a, b, c, d where a=b=c=d=[-Range,…Range]. This is so that I can sample as many points as possible, then set a conditional where it only graphs if its inside the fractal. I basically need a way to sample every possible point that could be in the mandelbulb and then only plot if its in the fractal.
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### Author:  [@Guzman\_Tierno](https://cl.desmos.com/u/Guzman_Tierno)
#### Post date: [October 4, 2025, 7:59pm UTC](https://cl.desmos.com/t/creating-lists-of-4d-points/8272/7 "2025-10-04T19:59:04Z")
The problem, if I understand the situation correctly, is that you represented a quaternion with a list [(a,b), (c,d)], that is: a list of two points.
So if you want to generate a grid of points you should do something like
[(a,b), (c,d)] for a=Range, b=Range, c=Range, d=Range
and this is not allowed because you would generate a list of lists (which are not supported in Desmos).
So you could represent a list of quaternions as a simple list of real values taking the elements of the list four at a time.
Otherwise you could use a function to generate all the possible values for points in your grid of quaternions, like this (see function Q):
[https://www.desmos.com/calculator/lrpvdv8dic](https://www.desmos.com/calculator/lrpvdv8dic)
for any integer value you get a quaternion of the grid
Does this help?
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### Author:  [@Daniel\_Grubbs](https://cl.desmos.com/u/Daniel_Grubbs)
#### Post date: [October 4, 2025, 9:49pm UTC](https://cl.desmos.com/t/creating-lists-of-4d-points/8272/8 "2025-10-04T21:49:39Z")
If I’m understanding correctly, which I don’t claim to, you want a set of unique four coordinate points? So, I’d [generate lists for each coordinate](https://www.desmos.com/calculator/vw9np5z8vf) (keeping the same order in each list comprehension is important), and function `Q_List` would return the set of coordinates at a particular index.
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### Author:  [@Guzman\_Tierno](https://cl.desmos.com/u/Guzman_Tierno)
#### Post date: [October 4, 2025, 9:54pm UTC](https://cl.desmos.com/t/creating-lists-of-4d-points/8272/9 "2025-10-04T21:54:28Z")
The four functions in this graph, r1 … r4 do generate the lists Daniel says …
And the function Q(k) gives you the k-th quaternion of the list:
[https://www.desmos.com/calculator/lrpvdv8dic](https://www.desmos.com/calculator/lrpvdv8dic)
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### Author:  [@Daniel\_Grubbs](https://cl.desmos.com/u/Daniel_Grubbs)
#### Post date: [October 4, 2025, 10:01pm UTC](https://cl.desmos.com/t/creating-lists-of-4d-points/8272/10 "2025-10-04T22:01:15Z")
So I’m just repeating the simplest part of @Guzman_Tierno ‘s. 😆
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### Author:  [@Loumen\_Cai](https://cl.desmos.com/u/Loumen_Cai)
#### Post date: [October 4, 2025, 10:08pm UTC](https://cl.desmos.com/t/creating-lists-of-4d-points/8272/11 "2025-10-04T22:08:18Z")
YESS!!
Thank you so much I think it works now but I havent implemented it yet
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### Author:  [@Guzman\_Tierno](https://cl.desmos.com/u/Guzman_Tierno)
#### Post date: [October 4, 2025, 10:09pm UTC](https://cl.desmos.com/t/creating-lists-of-4d-points/8272/12 "2025-10-04T22:09:26Z")
Here’s the same code in 3D:
[https://www.desmos.com/3d/ekfu5murgy](https://www.desmos.com/3d/ekfu5murgy)
But you can only have a cubic grid whose side is smaller than 10 because otherwise the list gets bigger than 10.000 elements and this is not supported.
You can use the slider s to see a projections of the quaternions moving.
You will have to do every calculation for the Mandelbulb component-wise
because you cannot have a list of quaternions.
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### Author:  [@Loumen\_Cai](https://cl.desmos.com/u/Loumen_Cai)
#### Post date: [October 4, 2025, 10:42pm UTC](https://cl.desmos.com/t/creating-lists-of-4d-points/8272/13 "2025-10-04T22:42:02Z")
I implemented in the original mandelbulb code and now it says “definitions are nested too deeply“
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### Author:  [@Loumen\_Cai](https://cl.desmos.com/u/Loumen_Cai)
#### Post date: [October 4, 2025, 10:42pm UTC](https://cl.desmos.com/t/creating-lists-of-4d-points/8272/14 "2025-10-04T22:42:09Z")
> **[\[Copy of\] \[Copy of\] Project #38b \[Mandelbulb Quaternion\]](https://www.desmos.com/3d/j0j0byn9e5)**
>
> Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.
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### Author:  [@Loumen\_Cai](https://cl.desmos.com/u/Loumen_Cai)
#### Post date: [October 4, 2025, 10:55pm UTC](https://cl.desmos.com/t/creating-lists-of-4d-points/8272/15 "2025-10-04T22:55:19Z")
Also the power function P(x, y) doesn’t seem to be working. It keeps on returning undefined, I think the problem is the M(y, ln(x)). The multiplication function isn’t working with the decimal outputs of the ln() function
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### Author:  [@Guzman\_Tierno](https://cl.desmos.com/u/Guzman_Tierno)
#### Post date: [October 5, 2025, 8:25am UTC](https://cl.desmos.com/t/creating-lists-of-4d-points/8272/16 "2025-10-05T08:25:17Z")
I’m sorry, there are too many things together and I can’t undestand how everything works.
I do not get the error “too deeply nested” … maybe you solved it … but on the other hand the graph doesn’t show anything.
Maybe you can start a new graph introducing things step by step …
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### Author:  [@Loumen\_Cai](https://cl.desmos.com/u/Loumen_Cai)
#### Post date: [October 5, 2025, 2:01pm UTC](https://cl.desmos.com/t/creating-lists-of-4d-points/8272/17 "2025-10-05T14:01:55Z")
I solved the grid problem but now i have a new problem which is the Definitions are nested too deeply problem. Am I supposed to make a new topic or can I use this one?
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### Author:  [@Guzman\_Tierno](https://cl.desmos.com/u/Guzman_Tierno)
#### Post date: [October 5, 2025, 2:07pm UTC](https://cl.desmos.com/t/creating-lists-of-4d-points/8272/18 "2025-10-05T14:07:54Z")
You can use this one …
I’m not getting that error … where and how do you get that error?
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### Author:  [@Loumen\_Cai](https://cl.desmos.com/u/Loumen_Cai)
#### Post date: [October 5, 2025, 9:25pm UTC](https://cl.desmos.com/t/creating-lists-of-4d-points/8272/19 "2025-10-05T21:25:17Z")
I get the nested too deeply error after I plug in everything into the iteration. Also, the power function isn’t working P(Q1, Q2)
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### Author:  [@Loumen\_Cai](https://cl.desmos.com/u/Loumen_Cai)
#### Post date: [October 5, 2025, 9:32pm UTC](https://cl.desmos.com/t/creating-lists-of-4d-points/8272/20 "2025-10-05T21:32:13Z")
Its in the link [R Project #38b [Mandelbulb Quaternion] | Desmos](https://www.desmos.com/3d/5cagnxkezo) . The problem can be found in the “Points“folder. I was testing out f(100) for the iterations, and it said definitions nested too deeply.
[Next page](https://cl.desmos.com/t/creating-lists-of-4d-points/8272.md?page=2)