Collatz Tree

collatz.jl

using CairoMakie
using LightGraphs
using GraphMakie
using NetworkLayout

function create_collatz_node_rec(g, n::Int, max_n::Int)
    child1n = n*2 
    if child1n <= max_n 
        add_edge!(g, n, child1n)
        create_collatz_node_rec(g, child1n, max_n)
    end
    if (n-1) % 3 == 0
        child2n = (n-1) ÷ 3
        if child2n > 1 && child2n <= max_n && child2n % 2 == 1
            add_edge!(g, n, child2n)
            create_collatz_node_rec(g, child2n, max_n)
        end
    end
    return
end

function build_tree(max_n)
    g = SimpleDiGraph(max_n)
    create_collatz_node_rec(g, 1, max_n)
    return g
end
function mylayout(g)
    layout = Buchheim()(g)
    l = map(layout) do p
         return Point2(p[1], p[2]*5.0)
    end
    return l
end

function main()
    fig = Figure(resolution=(500,1000))
    fig[1,1] = ax = Axis(fig)
    g = build_tree(100)
    intree = connected_components(g)[1]
    g = g[intree]
    nlabels_align = [(:center, :bottom) for v in vertices(g)]
    nlabels_offset = [Point2(0.0,0.0) for v in vertices(g)]
    nlabels = string.(intree)
    p = graphplot!(ax, g; layout=mylayout,
                              nlabels=nlabels,
                              nlabels_offset=nlabels_offset,
                              nlabels_align,
                              arrow_show=false
                              )
    hidedecorations!(ax); hidespines!(ax)
    xlims!(ax, -3, 3)
    ylims!(ax, -290, 10)
    for v in vertices(g)
        if isempty(inneighbors(g, v)) # root
            nlabels_offset[v] = Point2(0.0, 0.1)
        elseif isempty(outneighbors(g, v)) #leaf
            @show v
            nlabels_offset[v] = Point2(0.0,-8.0)
        else
            # check if child of a parent of two
            parent = inneighbors(g, v)[1]
            if length(outneighbors(g, parent)) == 2
                nlabels_offset[v] = Point2(0.0,0.2)
            else
                nlabels_offset[v] = Point2(0.12*length(nlabels[v]),-2.0)
            end

        end
    end
    p.nlabels_offset = nlabels_offset
    fname = "collatz_tree"
    save(fname, fig)
end