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Fibonacci256 price drop!
I messed up when copying the listing from Tindie to Lectronz. It's fixed now, resulting in a $120 drop in price. If you'd previously taken a look at the listing, you might want to take another look. Sorry about that! 😅
lectronz.com/products/fibonacc…

Fibonacci256 - 166mm disc with 256 HDR RGB LEDs

Fibonacci256 is a beautiful 166mm circular disc with 256 SK8922-EC20 HDR RGB LEDs surface mounted in a Fibonacci distribution.
lectronz.com
in reply to Jason Coon

Kernel Bob
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Kernel Bob
• •
Why do the lit areas have sharp pentagonal edges? Have you etched a Voronoi tiling into the diffuser?
in reply to Jason Coon

Jason Coon
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Jason Coon
• •
@kbob actually, sorry, that's a pic of the new "expanding" Fibonacci256.There's also a matching thin voronoi grid behind the black LED acrylic.
@Kernel Bob
in reply to Jason Coon

Kernel Bob
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Kernel Bob
• •

So I found these equation for fibonacci placement.

θₙ = 2πφⁿ
rₙ = sqrt(n) = n^(0.5)

Is that what you're using? For the expanding version, are you using the same θ and changing the exponent on r?

(So many questions!)

in reply to Jason Coon

Kernel Bob
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Kernel Bob
• •

I should have looked at your product description 😁 It's right there.

137.508° = 2π(2 - φ) radians

So my formula was rotating in the wrong direction. 2π(2-φ) (your angle) is congruent to -(2πφ) (my angle) mod 2π. The Golden Ratio makes my head hurt once again.

In disc phyllotaxis, as in the sunflower and daisy, the mesh of spirals occurs in Fibonacci numbers because divergence (angle of succession in a single spiral arrangement) approaches the golden ratio. The shape of the spirals depends on the growth of the elements generated sequentially. In mature-disc phyllotaxis, when all the elements are the same size, the shape of the spirals is that of Fermat spirals—ideally. That is because Fermat's spiral traverses equal annuli in equal turns. The full model proposed by H Vogel in 19791 is r=c sqrt(n), θ =n x 137.508°, where θ is the angle, r is the radius or distance from the center, and n is the index number of the floret and c is a constant scaling factor. The angle 137.508° is the golden angle which is approximated by ratios of Fibonacci numbers.
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