zooming parabola with infinitely inscribed triangles

animation.svg

script.py

#!/usr/bin/env python3

from math import log2


COLORS = ['#e50000', '#ff8d00', '#ffee00', '#028121', '#004cff', '#770088']

keyframes = 12  # can't be odd number!
per_kf = 4      # minimum = 4 (small filesize), otherwise for smooth animation
dur = 20        # longer animation need more per_kf



# ============================================================================

assert keyframes % 2 == 0
assert per_kf >= 4
lag = dur / keyframes


def pn(number):
    return str(round(number, 2))

def ppoly(trig):
    return ' '.join(','.join(map(pn, pair)) for pair in trig)

def pairwise(ls):
    return zip(ls, ls[1:])

def sign(xs, lvl, k=1/2**6):
    if lvl % 2 == 0:
        return [k*x for x in xs]
    return [-k*x for x in xs]

def mid(xs):
    return sum(xs)/2

def make_trig(xs, i=0):
    xs = [x * 2**(i/per_kf) for x in xs]
    return [(10*x, -x**2) for x in [mid(xs), *xs]]


def print_trig(xs, co, lvl):
    trigs = [make_trig(xs, i) for i in range(1+per_kf*keyframes)]
    print(f'<polygon points="0,0 0,0 0,0" stroke="{co}" fill="{co}">')
    print(f'<animate attributeName="points" begin="{pn(lvl*lag)}s" dur="{dur}s" repeatCount="indefinite"')
    print(f'values="{";".join(map(ppoly, trigs))}" />')
    print('</polygon>')


def print_main_trig(lvl=0):
    co = COLORS[(lvl+0)%len(COLORS)]
    xs = sign([-1, 2], lvl)
    print_trig(xs, co, lvl)


def print_acc_trig(lvl=0):
    co = COLORS[(lvl+1)%len(COLORS)]
    xs = sign([1/2, 2], lvl)
    print_trig(xs, co, lvl)


def print_surr_trigs(lvl=0):
    co = COLORS[(lvl+2)%len(COLORS)]
    xss = [sign(xs, lvl) for xs in pairwise([1/2, 5/4, 2])]
    for xs in xss:
        print_trig(xs, co, lvl)


def print_outer_trigs(lvl=0):
    co = COLORS[(lvl+3)%len(COLORS)]
    xss = [sign(xs, lvl) for xs in pairwise([1/2, 7/8, 5/4, 13/8, 2])]
    for xs in xss:
        print_trig(xs, co, lvl)



# ============================================================================

print('<svg xmlns="http://www.w3.org/2000/svg" width="600" height="600" viewBox="-200 -395 400 400">')

for i in range(keyframes):
    print_outer_trigs(-i)
    print_surr_trigs(-i)
    print_acc_trig(-i)
    print_main_trig(-i)

print('<path id="parabola" d="M -300,-900 Q 0,900 300,-900 M 900,-900 900,900 -900,900 -900,-900" fill="#fff" stroke="#000" />')

print('</svg>')