"""The four plates of the auctoritates leaves (imported by illum.py)."""
import math
from illum import (euclid, bits, f, plate_wrap, INK, TEXT, LAPIS, CINNABAR, GOLD, GOLD_LT,
GOLD_PALE, GOLD_DK, RULE, MATTER, MONO, SERIF)
def plate_rota(num='II', width=420):
"""THE WHEEL: rings of 16, 12, 8 and 4 steps, each E(k,n), spokes to the hub."""
c = width / 2
rings = [(16, 7, 186, GOLD), (12, 5, 140, LAPIS), (8, 3, 94, CINNABAR), (4, 1, 50, GOLD)]
out, spokes = [], []
for n, k, r, col in rings:
out.append(f'')
for i, on in enumerate(euclid(k, n)):
a = math.radians(-90 + 360 * i / n)
x, y = c + r * math.cos(a), c + r * math.sin(a)
if on:
spokes.append(f'')
out.append(f'')
else:
out.append(f'')
out.append(f'E({k},{n})')
out.append(f'')
out.append(f'')
svg = (f'')
cap = ('Quasi sit rota in medio rotae (Ez 1:16, Vulgate). Rings of sixteen, twelve, eight and four steps, each with its strokes '
'spread as evenly as they can be, and one in the middle. Every spoke runs to the hub and runs from it: culmen et fons (SC 10).')
return plate_wrap(num, 'Rota in medio rotae', svg, cap, width)
def plate_truchet(num='IV', width=420, word='APTATIO'):
"""ONE TILE, FOUR LAWS: a Truchet tile laid all alike, by row and column,
by the diagonals, and by the bits of the word."""
t = 29
n = 6
pw = n * t
gap = (width - 2 * pw) / 1
stream = ''.join(bits(word))
rules = [('all alike', lambda i, j, q: 0),
('by row and column', lambda i, j, q: 2 * (i % 2) + (j % 2)),
('by the diagonals', lambda i, j, q: 0 if (i + j) % 2 == 0 else 2),
(f'by the bits of {word}', lambda i, j, q: int(stream[(2 * q) % len(stream)] + stream[(2 * q + 1) % len(stream)], 2))]
out = []
for p, (lab, rule) in enumerate(rules):
ox = (p % 2) * (pw + gap)
oy = (p // 2) * (pw + 40)
for i in range(n):
for j in range(n):
q = i * n + j
o = rule(i, j, q)
x, y = ox + j * t, oy + i * t
corners = [(x, y), (x + t, y), (x + t, y + t), (x, y + t)]
a, b, cc = corners[o], corners[(o + 1) % 4], corners[(o + 3) % 4]
out.append(f'')
out.append(f'')
out.append(f'')
out.append(f'{lab}')
hv = 2 * pw + 40 + 24
svg = (f'')
cap = ('One tile, half lapis and half gold, laid by four laws: all alike; turned by row and column; turned by the diagonals; '
f'turned by the bits of {word}, two at a time. The tile is never altered, only the law of its laying. '
'Not a rigid uniformity, and still one tile (SC 37–38).')
return plate_wrap(num, 'Aptatio', svg, cap, width)
def plate_cell(num='VI', width=420):
"""A MEMORY CELL: two buffers in a ring, each feeding the other. Pushed
once on CREDENDI, SUPPLICANDI follows a step later, and both stay."""
out = []
L, R_ = 70, width - 70
yt, yb = 62, 150
ym = (yt + yb) / 2
def buf(x, y, right=True, s=34):
if right:
d = f'M {f(x - s / 2)} {f(y - s / 2)} L {f(x + s / 2)} {f(y)} L {f(x - s / 2)} {f(y + s / 2)} Z'
else:
d = f'M {f(x + s / 2)} {f(y - s / 2)} L {f(x - s / 2)} {f(y)} L {f(x + s / 2)} {f(y + s / 2)} Z'
return f''
mx = width / 2
wire = f'stroke="{INK}" stroke-width="1.4" fill="none"'
out.append(f'')
out.append(f'')
out.append(buf(mx, yt, True))
out.append(buf(mx, yb, False))
out.append(f'Indiculus 8: statuat')
out.append(f'Mediator Dei 48: statuat')
for x, lab, col, anc, dx in ((L, 'SUPPLICANDI', LAPIS, 'start', 10), (R_, 'CREDENDI', GOLD_DK, 'end', -10)):
out.append(f'')
out.append(f'{lab}')
# the push, into CREDENDI from the right
out.append(f'')
out.append(f'push')
# the timing: sixteen steps
tx0, tx1 = 92, width - 12
st = (tx1 - tx0) / 16
rows = [('push', CINNABAR, lambda s: 1 if s == 2 else 0),
('credendi', GOLD_DK, lambda s: 1 if s >= 2 else 0),
('supplicandi', LAPIS, lambda s: 1 if s >= 3 else 0)]
ty = 222
for s in range(17):
x = tx0 + s * st
out.append(f'')
for r, (lab, col, fn) in enumerate(rows):
y = ty + r * 30
out.append(f'{lab}')
pts, prev = [], None
for s in range(16):
v = fn(s)
yy = y - 12 * v + 6
x = tx0 + s * st
if prev is not None and prev != yy:
pts.append((x, prev))
pts.append((x, yy))
pts.append((x + st, yy))
prev = yy
d = 'M' + ' L'.join(f'{f(px)} {f(py)}' for px, py in pts)
out.append(f'')
hv = ty + 3 * 30 - 6
svg = (f'')
cap = ('Two buffers in a ring, each feeding the other: the Indiculus has the law of praying establish the law of believing, '
'Mediator Dei 48 has the law of believing establish the law of praying. A cell like this holds its bit only because each half keeps '
'telling the other what it is. Pushed once, on credendi, the other follows a step later and both stay: semel traditae sanctis fidei (Jude 3).')
return plate_wrap(num, 'Semel tradita', svg, cap, width)
def plate_staircase(num='VIII', width=420, mark=9):
"""EVERY RHYTHM OF SIXTEEN: E(k,16), k = 0 to 16. The first row is silence;
the row of the leaf's word (its letters) is the talea at its sides."""
cell = 19.5
x0, y0 = 46, 4
out = []
for k in range(17):
y = y0 + k * cell
pat = euclid(k, 16)
if k == 0:
out.append(f'')
if k == mark:
out.append(f'')
out.append(f'{k}')
for i, on in enumerate(pat):
x = x0 + i * cell
if on:
out.append(f'')
else:
out.append(f'')
out.append(f'silentium')
out.append(f'this leaf')
wv = width
hv = y0 + 17 * cell + 4
svg = (f'')
cap = ('Every rhythm of sixteen steps, from no stroke to sixteen, each spreading its strokes as evenly as it can among its rests. '
f'The first row is all silence; row {mark}, for the {mark} letters of SILENTIUM, is the talea at the sides of this leaf. '
'Suo quoque tempore sacrum silentium servetur (SC 30).')
return plate_wrap(num, 'Silentium', svg, cap, width)