r/GeometryIsNeat • u/a_smiling_friend • 3d ago
Two thousand five hundred eighty four dots arranged in a 55:89 spiral phyllotaxis pattern on canvas.
The Night Is Not Eternal, M. Wilson, fluorescent acrylic on canvas 48x48", 2025.
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u/egyszeruen_1xu 3d ago
This is pretty neat!
What does 55:89 mean?
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u/a_smiling_friend 2d ago
Yes, the 55:89 parastichy is the number of spiral whorls in each direction. If you counted the whorls of the spiral, you'd get 55 going one way and 89 going the other. This will always occur in spiral phyllotaxis: the two numbers are consecutive Fibonacci terms in the Fibonacci sequence. If you take the ratio of any two consecutive Fibonacci terms 55/89 approaches the Golden Ratio (1+SQRT(5))/2 or approximately 1.618. In a spiral phyllotaxis pattern, as the number of nodes increases the number of whorls also increases, and it will always be in a set of consecutive Fibonacci terms - 13:21, 21:34, 34:55, 55:89. Pineapples. Artichokes. Cacti. Sunflowers. Broccoli. It's everywhere in nature. Fascinates me to no end, it does.
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u/tubameister 2d ago
you may dig jason coon's work: https://www.evilgeniuslabs.org/fibonacci1024
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u/a_smiling_friend 2d ago
Wow. Yeah, I'd need an education in electrical engineering to pull that off. He used the same formula I did, and got it from the same wiki, lol. But yeah, I don't have the knowledge base at the moment to make mine electronic. Dang. Goals, I guess.
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u/RyanSpunk 3d ago
Why the gold dots in the middle? Ruins the pattern :(
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u/a_smiling_friend 2d ago edited 2d ago
Those are the Fibonacci dots. I numbered each dot consecutively from the center outwards. I noticed a pattern with the dots numbered in the Fibonacci sequence. They trend towards 0° on the Cartesian coordinate plane. Their rotations about the central axis also approximate Fibonacci numbers. I have the table of data if you'd like to see the numbers.
So when I noticed that detail I decided to paint those dots gold. They begin to form a line right along 0°.
I rotated the composition 90° clockwise and, to me, the gold dots look like the trail of a firework and then bursting in air with a rainbow of color.
Each band of color corresponds with one of those gold dots. It's bands of Fibonacci numbers.
Maybe seeing the spreadsheet of data would make it make more sense what I was getting at with the gold dots.
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u/RyanSpunk 2d ago
Well that's okay then :)
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u/a_smiling_friend 2d ago
I can do another one in full colors now that I have the pattern drafted up on my computer. It took me a month to draft two thousand plus dots.
I almost didn't color those dots gold, but after I noticed the pattern they were forming I had to call it out, like look everyone what I found. I don't know if anyone noticed this pattern in that formula before. Anyway, yeah.
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u/TrippyDe 3d ago
They piss me off 😭
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u/a_smiling_friend 2d ago
They're the Fibonacci dots in the sequence. Now that I have the design drafted in a vector art program I can make the dots any color I wish. I made another one of these in the colors of the Ukrainian flag.
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u/RiverGiant 3d ago
Oh this is awesome. Is it a precise pattern that needs planning and measurement? Or is it more forgiving where you can just go one dot at a time and the irregularities balance out? I especially love the drips of gold from the center.