factorTrees.sagews

import random
def ftree(rows, v, i, F):
    if len(v) > 0: # add a row to g at the ith level.
        rows.append(v)
    w = []
    for i in range(len(v)):
        k, _, _ = v[i]
        if k is None or is_prime(k):
            w.append((None,None,None))
        else:
            d = random.choice(divisors(k)[1:-1])
            w.append((d,k,i))
            e = k//d
            if e == 1:
                w.append((None,None))
            else:
                w.append((e,k,i))
    if len(w) > len(v):
        ftree(rows, w, i+1, F)
def draw_ftree(rows,font):
    g = Graphics()
    for i in range(len(rows)):
        cur = rows[i]
        for j in range(len(cur)):
            e, f, k = cur[j]
            if not e is None:
                if is_prime(e):
                     c = (1,0,0)
                else:
                     c = (0,0,.4)
                g += text(str(e), (j*2-len(cur),-i), fontsize=font, rgbcolor=c)
                if not k is None and not f is None:
                    g += line([(j*2-len(cur),-i), ((k*2)-len(rows[i-1]),-i+1)],
                    alpha=0.5)
    return g

@interact
def factor_tree(n=100, font=(10, (8..20)), redraw=['Redraw']):
    n = Integer(n)
    rows = []
    v = [(n,None,0)]
    ftree(rows, v, 0, factor(n))
    show(draw_ftree(rows, font), axes=False)

Interact: please open in CoCalc