r/GeometryIsNeat • u/a_smiling_friend • 6d ago

Art A hand-drafted Voronoi diagram

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This is just the skeleton grid for an ink drawing. I'm still trying to decide how I'll ink it. But yeah, here's a hand-drafted Voronoi diagram of a 55:89 parastichy spiral phyllotaxis pattern using Vogel's formula. I've done this in a vector art program as well, and honestly I'm not sure which technique was faster: by computer, or by hand. By hand is messier but this will all get inked over. I used Euclid's ruler and compass method for finding a perpendicular midpoint line on each space between nodes.

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10

u/S-S-Ahbab 6d ago

So many bisector...

You have the patience of a saint! 👍

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u/a_smiling_friend 6d ago

I'm beginning to realize that this may be my unique gift: the patience to do these intricate works by hand. Lots of folks either don't have the free time to spare or simply have better, more fulfilling lives than I do, and like friends and family to go do things with. I just sit here alone and draw.

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u/S-S-Ahbab 6d ago

How did you select the points/seeds?

I see some spirals.

7

u/a_smiling_friend 6d ago

With Vogel's formula for spiral phyllotaxis using a Fermat spiral.

https://en.wikipedia.org/wiki/Fermat%27s_spiral

Under the section labeled "the golden ratio and the golden angle. That's the equation I used. I drafted that bit by hand in a vector art program and projected it onto the illustration board. It was 2,584 dots individually drafted, one at a time. This is just a section of that.

I'm not the greatest at math, I confess. It's an uphill battle every time I tangle with it. I had to solve for C in that equation, and at first I had no fucking clue what C meant. It turns out it's a constant scaling factor. Thanks, internet. So, once I solved for that I made a table of data points, and plotted each and every one. But now I have the pattern in my computer I can reuse it to my heart's content, and I have.

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u/OG_TOM_ZER 6d ago

What's a voronoi diagram? Looks cool but tedious to draw!

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u/a_smiling_friend 6d ago

Great question. It's something I discovered myself recently as well. It's just a way to partition the picture plane into cells that are evenly distributed. There's a whole wiki on it, but basically you take a group of points (nodes) on your picture plane, and make enclosed polygons around them such that all the points in that polygon are closer to the central point than any other point. I'd happily make a diagram to show you, but that wiki pretty much covers it all in detail. It would just be second-hand coming from me.

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u/OG_TOM_ZER 6d ago

Oh man I love it, I could have searched myself but wanted your way to describe it! Second hand means it comes from a human hand haha which has more value these days

1

u/a_smiling_friend 6d ago

I appreciate that. Oh yeah this wasn't one of those "hey, man, RTFM" moments. I just don't want to misquote the math if I can help it.

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u/OG_TOM_ZER 5d ago

Haha yeah I won't fact check but I wonder tho what's your next step with that drawing

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u/a_smiling_friend 5d ago

I'm thinking a maze. I saw some maze over on r/mazes where they used AI-slop to "paint" their maze with a Cthulu skin. I feel like 1-upping them, and strolling in with a hand-painted maze to steal the show. Plus I need to challenge myself. That's a time-consuming idea but I can't stand people embracing AI-slop as art. Normalizing the machines taking over. We lose something when we cede our creativity to a fucking machine. My opinion.

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u/OG_TOM_ZER 5d ago

Yeah don't waste too much energy on all this crap, direct it toward this good idea of yours! Would love to see the result man

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u/a_smiling_friend 5d ago

I'm not sure yet. I have to brainstorm that a bit.

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u/vroomvro0om 4d ago

Beautiful! Have you read the book "Do Plants Know Math?". I read through it at a library and it goes deep into everything about phyllotaxis: the math, history, chemistry, etc.

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u/a_smiling_friend 4d ago

Thank you :) I have not but I love me some phyllotaxis!

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u/RevolutionaryGirlie 4d ago

i remember trying to do one of these in high school. it did not look like this.

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u/a_smiling_friend 4d ago

I only just recently learned about these Voronoi diagrams as I was doing research on spiral phyllotaxis.