Spirals

This started when Kristoff wanted to pain patterns on maps depicting sandy soils. See the all story in this Forum discussion

11.1 μs

Archimedean spiral

From https://en.wikipedia.org/wiki/Archimedean_spiral

9.0 μs

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using GMT

683 ms

The begin end of this block are NOT the GMT's modern mode gmt begin ... gmt end. They are forced by the Nootebook to have more than one command per cell.

1.8 ms

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begin
    # Play arround with these parameters
    T = 1;
    omega = 2pi / T;
    v = 0.2;
    t = 0:0.01:5pi;
    x = v.*t .* cos.(omega .* t);
    y = v.*t .* sin.(omega .* t);
end;

101 μs

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plot(x, y, aspect=:equal, show=true)

777 ms

Fermati spiral

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md"## Fermati spiral"

5.6 μs

x
 
θ = 0:0.01:5pi;

4.4 μs

x
 
xf = sqrt.(θ) .* cos.(θ);

60.0 ms

x
 
yf = sqrt.(θ) .* sin.(θ);

64.5 ms

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plot(xf,yf, aspect=:equal, show=true)

747 ms

Sunflower

From This FEX contribution. The author here wanted to reflect the fact that on a sunflower the seeds close to the center are smaller and have a higher density.

10.8 μs

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phi = (sqrt(5)-1)/2;

100 ns

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n = 2618;

0.0 ns

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rho = (2:n-1) .^ phi;

136 μs

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theta = (2:n-1)*2pi*phi;

1.5 μs

x
 
scatter(rho .* cos.(theta), rho .* sin.(theta), marker=:point, aspect=:equal, show=true)

786 ms

Another Sunflower

This one was reversed from the javascript in this page, which follows the original work of Helmut Vogel in A better Way to Construct the Sunflower Head, where he proposed that spiral branches of seeds in a sunflower head are added from the center at an angle of 137.5∘ from the preceding one.

This time we will also color the seed points in function of r, the distance to the center and pain with a dark background.

47.7 μs

x
 
begin
    angle = 137.5;  # Play with this angle between [137.0 138.0]. Amazing the effect, no?
    alfa = 2pi * angle / 360;
    n_seeds = 1500;
    seeds = 0:n_seeds;
    r = sqrt.(seeds);
    ϕ = alfa * seeds;
    C = makecpt(range=(1,sqrt(n_seeds),1), cmap=:buda); # Color map to paint the seeds
    scatter(r .* cos.(ϕ), r .* sin.(ϕ), marker=:point, cmap=C, zcolor=r,
        frame=(fill=20,), aspect=:equal, show=true)
end

932 ms