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@neizod
Created July 27, 2022 01:24
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zooming parabola with infinitely inscribed triangles
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#!/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>')
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