Mandelbrot set: Difference between revisions

Line 6,687:

savefig("Mercator_Mandelbrot_deep_map.png")</syntaxhighlight>

Due to abs(z - epsilon) < 2 and the second reference sequence, Z and dZ can be calculated after the loop. This massively reduces the computing time.

'''Speed improvement:''' Due to abs(z - epsilon) < 2 and the second reference sequence, Z and dZ can be calculated after the loop. This massively reduces the computing time.

<syntaxhighlight lang=julia>Z, dZ, E, dE = zero(C), zero(C), zero(C), zero(C)

D, I = zeros(size(C)), ones(Int64, size(C))

Line 6,703:

D[N] = 0.5 .* log.(abs.(Z[N])) .* abs.(Z[N]) ./ abs.(dZ[N])</syntaxhighlight>

Another approach to reducing glitches is rebasing. See [https://gbillotey.github.io/Fractalshades-doc/math.html#avoiding-loss-of-precision Avoiding loss of precision] (Fractalshades) and [https://fractalforums.org/fractal-mathematics-and-new-theories/28/another-solution-to-perturbation-glitches/4360 Another solution to perturbation glitches] (Fractalforums) for details.

'''Quality improvement:''' Another approach to reducing glitches is rebasing. See [https://gbillotey.github.io/Fractalshades-doc/math.html#avoiding-loss-of-precision Avoiding loss of precision] (Fractalshades) and [https://fractalforums.org/fractal-mathematics-and-new-theories/28/another-solution-to-perturbation-glitches/4360 Another solution to perturbation glitches] (Fractalforums) for details.

<syntaxhighlight lang=julia>Z, dZ, E = zero(C), zero(C), zero(C)

D, I, J = zeros(size(C)), ones(Int64, size(C)), ones(Int64, size(C))

iteration(S, E, C) = (2 .* S .+ E) .* E .+ C

for k in 1:n # you can also try 1:2n or 1:5n due to rebasing

for k in 1:n

M = abs2.(Z) .< abs2(r)

E[M] = iteration(S[I[M]], E[M], C[M])