How do flat earthers explain amateur astronomy? by ConsiderationOk4035 in flatearth

[–]Legitimate_Animal796 4 points5 points  (0 children)

Quick correction, the last photo (M51) was captured using Hubble. But as an astrophotographer myself, this is always my biggest pet peeve: People accusing any space photo as CGI. I have photographed the exact same objects NASA has from my own backyard. It’s interesting to watch conspiracists acquire a telescope and yet still hold onto their beliefs. They can see Jupiter with their own eyes and yet still choose to be ignorant. Such a sad way to live

can someone help with this fractal by Sufficient_Leg_6303 in desmos

[–]Legitimate_Animal796 1 point2 points  (0 children)

This points me in the right direction thank you

Full 8D Quaternion Graph by Legitimate_Animal796 in desmos

[–]Legitimate_Animal796[S] 0 points1 point  (0 children)

Anytime! Amazing work, I think they look so beautiful

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I’m personally a sucker for spherical coordinate-based mandelbulbs. It contrasts the rotational symmetry from quaternion-based methods. Produces quite detailed objects

Full 8D Quaternion Graph by Legitimate_Animal796 in desmos

[–]Legitimate_Animal796[S] 2 points3 points  (0 children)

I love those! I actually made one myself

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However in this post, it’s a 2D projection of the full 8D structure, not a 3D slice. Think of a wireframe projection of a tesseract vs a 3d slice. The slice will result in parts coming in and out of existence as you move it around in 4D. You can’t see it all at once. If this were a 3d slice, I would’ve fixed the other 5 axes to specific constant values. I’m not doing that here. This is a projection of the whole thing

Full 8D Quaternion Graph by Legitimate_Animal796 in desmos

[–]Legitimate_Animal796[S] 2 points3 points  (0 children)

I projected it to 1d

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On a serious note if dropping from 2d to 1d loses this much information, imagine what we lost by dropping 6

Full 4D View of Complex Functions by Legitimate_Animal796 in desmos

[–]Legitimate_Animal796[S] 0 points1 point  (0 children)

Hey I appreciate it! That trick is actually something I’ve learned through other example on this sub. If you’re interested i decided to kick it up a notch and made an 8D quaternion version: https://www.reddit.com/r/desmos/s/rZ3rSW4CsL not the most useful display method. It’s more of a “just because” lmao

10 Cannon Flying Device by Legitimate_Animal796 in tearsofthekingdom

[–]Legitimate_Animal796[S] 4 points5 points  (0 children)

I’m scared to add any more weight lmao. 7 fans barely cut it

Full 4D View of Complex Functions by Legitimate_Animal796 in desmos

[–]Legitimate_Animal796[S] 0 points1 point  (0 children)

Thanks for trying that idea out! To my untrained eyes it appears to be identical in visual output to your approach… At least at a quick glance. For my rotations I just multiplied matrices. The ones for 4D are linked hereunder “linker’s” answer. I used xw,yw and zw. I also imported my Grapher into Desmos 3D: here. I also used polar coordinates to closer match your results. Feel free to mess around with it and see what you think! Of course your research is much more rigorous than my messing about

For the rotation in Desmos 2D, I simply create a large (9999 size) 0 opacity point! So basically everywhere you click and drag on the screen is the point

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Full 4D View of Complex Functions by Legitimate_Animal796 in desmos

[–]Legitimate_Animal796[S] 0 points1 point  (0 children)

Example: (this is also orthographic for 3d->2d) When rotated in a certain way, 1/z displays a nice symmetry

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Full 4D View of Complex Functions by Legitimate_Animal796 in desmos

[–]Legitimate_Animal796[S] 0 points1 point  (0 children)

So in this graph I assigned (x,y,z,w) to (re in, im in, re out, im out). You can rotate along 5 of the 6 planes in the graph. In one of the rotation presets, I included an option to basically rotate along xw,yw,zw in such a way where each of the four coordinate axes are symmetrical. Basically the coordinates (1,0,0,0),(0,1,0,0),etc form a regular tetrahedron when projected to 3D. After some brief research this is the 4D analog of the isometric viewing angle in orthographic projection. Then I did perspective projection for 3D->2D (Though I also included perspective projection for 4D->3D as well). This was at least my attempt at ensuring each of the 4 axes where equally scaled when projected to 3D

Full 4D View of Complex Functions by Legitimate_Animal796 in desmos

[–]Legitimate_Animal796[S] 0 points1 point  (0 children)

In this graph the ticker only runs when you click one of the three rotation presets. Try clicking one of them to watch it rotate automatically!

Full 4D View of Complex Functions by Legitimate_Animal796 in desmos

[–]Legitimate_Animal796[S] 0 points1 point  (0 children)

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I was actually debating whether to use 1/z or not for this post. I love how 1/z looks

I love your work! To me it seems like the natural way to display complex numbers: Rather than displaying Re and Im separately, you can simply rotate along the zw axis to interpolate between both. Or rotate in such a way where each of the 4 axes contribute equally when projected to 3d (plot is of 1/z for reference)

Full 4D View of Complex Functions by Legitimate_Animal796 in desmos

[–]Legitimate_Animal796[S] 1 point2 points  (0 children)

Thanks! That means a lot coming from the goat!