fBM.jl

# generate fractional Brownian motion (fBM)
# reference: https://thebookofshaders.com/13 by Patricio Gonzalez Vivo

using LinearAlgebra
using Images, FileIO

function fract(x)
    x - floor(x)
end

function random(vec)
    return fract(sin(dot(vec, [12.9898,78.233])) * 43758.5453123);
end

function mix(x, y, a)
    x * (1 - a) + y * a
end

function noise(vec)
    i = floor.(vec)
    f = fract.(vec)

  # Four corners in 2D of a tile
    a = random(i)
    b = random(i .+ [1.0, 0.0])
    c = random(i .+ [0.0, 1.0])
    d = random(i .+ [1.0, 1.0])

    u = f .* f .* (3.0 .- 2.0 * f)

    mix(a, b, u[1]) + (c - a) * u[2] * (1.0 - u[1]) + (d - b) * u[1] * u[2]
end

function fbm(vec, octaves=6)
  # Initial values
    value = 0.0
    amplitude = 0.5
    frequency = 0.0

  # Loop of octaves
    for i in 1:octaves
        value = value + amplitude * noise(vec)
        vec = vec .* 2
        amplitude = amplitude * 0.5
    end

    value
end

function main()
    width  = 320
    height = 320

    xy = collect.(Iterators.product(collect(0:width - 1) ./ width, collect(0:height - 1) ./ height))

    pix = zeros(RGB{Normed{UInt8,8}}, width, height, 30)

    for i in 1:30
        pix[:, :, i] = RGB.(fbm.(xy .* 3.0))
    end


    save("fbm.gif", permutedims(pix, (2, 1)))
end

main()