Mandelbrot set: Difference between revisions
m
→Normal Map Effect, Mercator Projection and Perturbation Theory: Zoom center changed and appropriate animation linked. Order of calculations adjusted.
m (→Normal Map Effect, Mercator Projection and Deep Zoom Images: Zoom center changed and appropriate animation linked. Order of calculations adjusted.) |
m (→Normal Map Effect, Mercator Projection and Perturbation Theory: Zoom center changed and appropriate animation linked. Order of calculations adjusted.) |
||
Line 8,000:
savefig("Mandelbrot_normal_map_2.png")</syntaxhighlight>
A small change in the code above creates Mercator maps and zoom images of the Mandelbrot set. See also the album [https://www.flickr.com/photos/arenamontanus/albums/72157615740829949 Mercator Mandelbrot Maps] by Anders Sandberg. See also [https://commons.wikimedia.org/wiki/File:Mandelbrot_sequence_new.gif ''Mandelbrot sequence new''] (Wikimedia) for a zoom animation to the given coordinates.
<syntaxhighlight lang="julia">using Plots
gr(aspect_ratio=:equal, axis=true, ticks=true, legend=false, dpi=200)
d, h = 200,
n, r =
a = -.743643887037158704752191506114774 # real coordinate of the zoom center
b = 0.131825904205311970493132056385139 # imaginary coordinate of the center
x = range(0, 2, length=d+1)
Line 8,011 ⟶ 8,014:
A, B = collect(x) .* pi, collect(y) .* pi
C =
Z, dZ = zero(C), zero(C)
Line 8,024 ⟶ 8,027:
D[N] = log.(abs.(Z[N])) .* abs.(Z[N]) ./ abs.(dZ[N])
heatmap(D' .^ 0.
savefig("Mercator_Mandelbrot_map.png")
Line 8,050 ⟶ 8,053:
a = BigFloat("-1.256827152259138864846434197797294538253477389787308085590211144291")
b = BigFloat(".37933802890364143684096784819544060002129071484943239316486643285025")
x = range(0, 2, length=d+1)▼
y = range(0, 2 * h / d, length=h+1)▼
A, B = collect(x) .* pi, collect(y) .* pi▼
S = zeros(Complex{Float64}, n+1)
Line 8,063 ⟶ 8,072:
end
end
▲x = range(0, 2, length=d+1)
▲y = range(0, 2 * h / d, length=h+1)
▲A, B = collect(x) .* pi, collect(y) .* pi
▲C = (- 4.0) .* exp.((A' .+ B .* im) .* im)
E, Z, dZ = zero(C), zero(C), zero(C)
| |||