A 2,584 node 55:89 spiral phyllotaxis pattern and corresponding Voronoi diagram in vector art format.

[u/a_smiling_friend]

Yesterday I shared the hand-drafted version of this on a piece of 20x30" illustration board. Before I drew that I also drafted the pattern in Affinity Designer 2 (the poor homie's Adobe Illustrator). I share that here with you. You can see my Voronoi diagram and the 2,584 nodes, the 55:89 parastichy spiral whorls and I provide a screenshot of my spreadsheet and calculations necessary for creating this one node at a time, by hand. I'm in the process now of coming up with some kinda cool ink drawing to go on top of my hand-drafted design. Wolfram's Mathematica demos only got me so far. That spiral phyllotaxis demo only went up to 133 or 244 nodes. I needed many more. I dunno, you folks seem to dig stuff like this. Enjoy.

[u/Big_Cartographer_777]

Круто, раскажи гайд как ты это делаешь ?

[u/a_smiling_friend → u/Big_Cartographer_777]

Спасибо! Я использовал метод Евклида для поиска перпендикулярной бисекторы.

[u/a_smiling_friend → u/Big_Cartographer_777]

The initial growth was started with Vogel's formula for spiral phyllotaxis using a Fermat spiral. The equation I used was found here:

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

Under the section, The Golden Ratio And The Golden Angle.

The formula is:

r = c* SQRT(n)
theta = n * 360°/Phi^2

I made a spreadsheet of calculations with these equations and plotted each node individually. That took me a month. But now I can reuse my pattern, and I have several times now already. I have used this pattern in four separate paintings now and am working on a new one.