Notes for a blog covering an introduction to julia using julia sets

Julia_and_Julia_sets_blog_notes.jl

#Pkg.add("Plots")
#Pkg.add("GR")
using Plots


@everywhere function pixel_color(x, y, width, height, c)
    max_iter = 255
    z = ( ((y/width)*2.7 - 1.3) + ((x/height)*4.5 - 2.5) *im )
    for iter_nr = 1:max_iter
        z = z^2 + c
        if abs(z) >= 4
            return iter_nr
        end
    end
    return -255
end


@everywhere function julia_set(height, width, c)
	jset = Array{Int32}(height, width)
    println("Generating set !")
	for x = 1:height
		for y = 1:width
			jset[x, y] = pixel_color(x, y, width, height, c)
		end
	end
    jset
end


function run()
    height = 1380
    width = 1380
    #c = 0.7885e ^ (0.8im)
    #data = julia_set(height, width, c)
    #hm = heatmap(data, size=(width,height), color=:ice)
    #png("/tmp/julia_$(height)_$(width)")
    nr_frames = 300

    sets = @sync @parallel append! for n=0:nr_frames
        c = e ^ (2*π*n/nr_frames*im)
        set = julia_set(height, width, c)
        [set]
    end

    anim = @animate for set in sets
        heatmap(set, size=(width,height), color=:inferno, leg=false)
    end

	gif(anim, "/tmp/julia_$(height)_$(width)_inferno2.gif", fps=15)
end


function mandelbrot_set()
    height = 2000
	width  = 2000
	max = 300
	mset = Array{Int32}(height, width)
    println("Generating set !")
	for x = 1:height
		for y = 1:width
			c = ( (y - width/2) * (4/width) + ((x - height/2) * (4/width))*im )
            z = (0 + 0im)
			current_iter = nothing
			for iter = 1:max
				current_iter = iter
				z = z^2 + c
				if abs(z) > 4
					break
				end
			end
			mset[x, y] = current_iter
		end
	end
    println("Ploting !")
	heatmap(mset, size=(width,height))
	png("/tmp/mandelbrot_$(height)_$(width)_$(max)")
end


function mandelbrot_set_para()
	height = 5000
	width  = 5000
	max = 255
    println("Generating set !")
	mset = @sync @parallel (hcat) for x = 1:height
        col =  Array{Int32}(width)
		for y = 1:width
			c = ( (y - width/2) * (4/width) + ((x - height/2) * (4/width))*im )
			z = (0 + 0im)
			current_iter = nothing
			for iter = 1:max
				current_iter = iter
				z = z^2 + c
				if abs(z) > 4
					break
				end
			end
			col[y] = current_iter
		end
        col
	end
    println("Ploting !")
	heatmap(mset, size=(width,height))
	png("/tmp/mandelbrot")
end


function lorenz_attractor()
	# initialize the attractor
	n = 300
	dt = 0.02
	σ, ρ, β = 10., 28., 8/3
	x, y, z = 1., 1., 1.

	# initialize a 3D plot with 1 empty series
	plt = path3d(1, xlim=(-25,25), ylim=(-25,25), zlim=(0,50),
	                xlab = "x", ylab = "y", zlab = "z",
	                title = "Lorenz Attractor", marker = 1,
					linecolor=RGBA(162/255,72/255,72/255,1/1))

	# build an animated gif, saving every 10th frame
    gui()
	@gif for i=1:n
	    dx = σ*(y - x)
		x += dt * dx

	    dy = x*(ρ - z) - y
		y += dt * dy

	    dz = x*y - β*z
		z += dt * dz

	    push!(plt, x, y, z)
	end every 10
end


function layer(x0, y0, z0, n)
    x,y,z = -0.3,0.2,0.11
    for i in 1:46
        r = sqrt(x^2 + y^2 + z^2)
        φ = atan2(y, x)
        θ = atan2(sqrt(x^2 + y^2), z)

        x = r^n * sin(n*θ)*cos(n*φ) + x0
        y = r^n * sin(n*θ)*sin(n*φ) + y0
        z = r^n * cos(n*θ) +z0

        if sum([x^2,y^2,z^2]) >= 2
            #println("$x0  $y0  $z0  $i")
            return 259 - i * 4
        end
    end
    return 0
end


function try_3d()
    xmax, ymax, zmax = 280, 280, 140
    colors = Array{RGBA}(xmax*ymax*zmax)
    X = Array{Int32}(xmax*ymax*zmax)
    Y = Array{Int32}(xmax*ymax*zmax)
    Z = Array{Int32}(xmax*ymax*zmax)

    i = 0
    for x in 1:xmax
        for y in 1:ymax
            for z in 1:zmax

                i += 1
                color = layer((1.8*x/xmax) - 0.9, (1.8*y/ymax) - 0.9, z/zmax, 8)

                transparency = 60
                if color >= 255
                    transparency = 0
                elseif color > 200
                    transparency = 2 * ( 255/color )
                end

                R = color
                B = color
                G = color

                if color < 255 && color > 120
                    B = B/5
                elseif color > 60 && color <= 120
                    R = R/2
                    B = B/2
                    G = G*1.2
                    if G > 250
                        G = 250
                    end
                elseif color <= 60
                    R = (R + 4)*10
                    if R > 250
                        R = 250
                    end
                    B = B/2
                    G = G/2
                end

                colors[i] = RGBA(R/255, G/255, B/255, transparency/255)
                X[i] = x
                Y[i] = y
                Z[i] = z

            end
        end
    end

    println("Plotting !")
    scatter3d(X,Y,Z,leg=false,cbar=true,w=5, c=colors, m=(1,0.0,colors,stroke(0)))
    png("/tmp/nest2")
end


#pyplot()
#run()