Mandelbrot set: Difference between revisions

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direction, height = 45, 1.5 # direction and height of the incoming light

stripes, damping = ~~5.0~~, 2.0 # stripe density and damping parameter

stripes, damping = 10, 2.0 # stripe density and damping parameter

x = range(0, 2, length=d+1)

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end

N = abs.(Z) .> 2 # ~~exterior~~ ~~distance~~ ~~estimation~~

N = abs.(Z) .>= r # normal map effect 1 (potential function)

D[N] = log.(abs.(Z[N])) .* abs.(Z[N]) ./ abs.(dZ[N])

heatmap(D .^ 0.1, c=:balance)

savefig("Mandelbrot_distance_est.png")

N = abs.(Z) .> 2 # normal map effect 1 (potential function)

P, Q = S[N] ./ T[N], (S[N] .+ sin.(stripes .* angle.(Z[N]))) ./ (T[N] .+ 1)

F = ~~1 .-~~ log2.(log.(abs.(Z[N])) ./ log(r))

F = log2.(log.(abs.(Z[N])) ./ log(r)) # fraction between 0 and 1 (for interpolation)

H = P .+ (Q .- P) .* F .* F .* (3 .- ~~2 .* F~~) ~~# hermite interpolation~~

H = F .* P .+ (1 .- F) .* Q # height perturbation (by linear interpolation)

U = Z[N] ./ dZ[N] # normal vectors to the equipotential lines

U, v = U ./ abs.(U), exp(direction / 180 * pi * im) # unit normal vectors and unit 2D vector

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savefig("Mandelbrot_normal_map_1.png")

N = abs.(Z) .> 2 # normal map effect 2 (distance estimation)

N = abs.(Z) .>= r # normal map effect 2 (distance estimation)

U = Z[N] .* dZ[N] .* ((1 .+ log.(abs.(Z[N]))) .* conj.(dZ[N] .^ 2) .- log.(abs.(Z[N])) .* conj.(Z[N] .* ddZ[N]))

U, v = U ./ abs.(U), exp(direction / 180 * pi * im) # unit normal vectors and unit 2D vector