koch.jl

# Modified from @frank's code at Discord

function koch_curve!(X, Y, x1, y1, x2, y2, level)
    if level == 0
        push!(X, x1)
        push!(X, x2)
        push!(Y, y1)
        push!(Y, y2)
    else
        Δx = x2 - x1
        Δy = y2 - y1
        x3 = x1 + Δx / 3
        y3 = y1 + Δy / 3
        x5 = y1 + 2Δx / 3
        y5 = y1 + 2Δy / 3
        x4 = ((x1 + x2) / 2) - ((Δy / 2) * sqrt(3))
        y4 = ((y1 + y2) / 2) + ((Δx / 2) * sqrt(3))
        koch_curve!(X, Y, x1, y1, x3, y3, (level - 1))
        koch_curve!(X, Y, x3, y3, x4, y4, (level - 1))
        koch_curve!(X, Y, x4, y4, x5, y5, (level - 1))
        koch_curve!(X, Y, x5, y5, x2, y2, (level - 1))
    end
end

X = []
Y = []
koch_curve!(X, Y, 1.0, 2.0, 0.0, 1.0, 2)

#=
julia> [X Y]
32×2 Matrix{Float64}:
 1.0       2.0
 0.888889  1.88889
 0.888889  1.88889
 1.12201   1.54466
 1.12201   1.54466
 1.77778   1.77778
 1.77778   1.77778
 0.666667  1.66667
 0.666667  1.66667
 ⋮         
 1.33333   1.33333
 1.33333   1.33333
 0.888889  1.22222
 0.888889  1.22222
 0.955342  0.0119661
 0.955342  0.0119661
 0.444444  1.11111
 0.444444  1.11111
 0.0       1.0
=#