begin

    using Markdown

    using Luxor

    using Colors

    using PlutoUI

end

f((x,y)) = (cos(y)^5*3^x, x^3+y) .|> p -> mod(p,1);

g((x,y)) = let a=2.1, b=5.9

    (sin(x*y/b)*y + cos(a*x - y), x + sin(y)/b) .|> p -> mod(p,1)

end;

arnold((x,y)) = (2x + y, x + y) .% 1;

function compose(f, n)

    function (x)

        val = x

        for _ in 1:n

            val = f(val)

        end

        return val

    end

end;

Base.:^(f::Function, n::Integer) = compose(f,n);

dist((x1,x2),(y1,y2)) = sqrt((x1-y1)^2 + (x2-y2)^2);

function dyndist(x,y,f,n)

    d = dist(x,y)

    for _ in 1:n

        x = f(x)

        y = f(y)

        d = max(d, dist(x,y))

    end

    d

end;

Np = 800

@bind cut Slider(0:0.01:1)

@bind n Slider(0:1:20)

p = (.671,.81);

fun = f;

let s = 800

    Drawing(s, s, "my-drawing.png")

    background("antiquewhite")

    for x in 0:(1/Np):1, y in 0:(1/Np):1

        x = rand() # * .01 + p[1] - .005

        y = rand() # * .01 + p[2] - .005

        let (tx,ty) = (fun^n)((x,y))

            setcolor(HSV(360tx,.5ty,dyndist((x,y),p,fun,n)))

        end

        if dyndist((x,y),p,fun,n) < cut

            setcolor("black")

        end

        circle(Point(s .* (x, y)), sqrt(s)*0.026, :fill) # .+ (.005,.005) .- p

    end

    setcolor("red")

    circle(s .* Point(p), 5, :fill) # Point(.5,.5)

    finish()

    preview()

end