[OC] Logistic Curve Windmills

I was playing with the logistics curve fractal, plotted it out to both negative and positive extents – it’s relatively straightforward if maths is your thing, I decided that I thought one arm of the logistics curve looked like a windmill blade, and I wondered what it would look like if I completed the pattern, by mirroring and duplicating the curve at 45 degree turns, so 8 arms in all.

And finally, wrapped in a circle with standard COS and SIN functions.

The “n” at the top of the page are scaling factors applied to each cross, they warp and size the two crosses, set in the sheet to randomise. There is an infinite number of these patterns that can be created.

The plot is straightforward scatter plot, markers only, the default circle reduced to point size 2 (the smallest) and border remove, coloured dark grey with 80% transparency.

I really love how it looks almost hand drawn, it’s the overlapping points across the 8 curves along with the 80% transparency, very much like say cross hatching pencil drawing to introduce shade

This is for the curve itself, let me know if you’d like me to provide rest of details for the plot, but just as described.

““ Excel

=LET(

λMin, -2,

λMax, 4,

λSteps, 3500,

x0, 0.5,

burnIn, 400,

keep, 80,

blowup, 1E6,

lambdas, SEQUENCE(λSteps, 1, λMin, (λMax-λMin)/(λSteps-1)),

orbit, LAMBDA(λ, SCAN(

x0, SEQUENCE(burnIn+keep,1),

LAMBDA(prev,_, LET(

next, λ*prev*(1-prev),

IF(ABS(prev)>blowup, NA(), next)

)))),

tail, LAMBDA(col, TAKE(col, -keep)),

pts, DROP(

REDUCE({0,0}, lambdas,

LAMBDA(acc, λ, LET(

xs, tail(orbit(λ)),

VSTACK(acc, HSTACK(λ+0*xs, xs))

))

),1),

pts

)