#!/usr/bin/env python3
"""bazaar.abaj.ai orb — milky-marble ground, golden dynamical-system flow, matte shading.

Family style of the sibling icons (matplotlib figure clipped to a circle, 612pt).
A damped two-vortex flow is integrated by hand (RK4) so line density stays airy;
trajectories are drawn as tapering gold strokes over marble veining, then a
radial matte falloff turns the disc into an orb.
"""

import numpy as np
import matplotlib

matplotlib.use('Agg')
import matplotlib.pyplot as plt
from matplotlib.collections import LineCollection
from matplotlib.colors import LinearSegmentedColormap, to_rgb

rng = np.random.default_rng(7)

IVORY = '#fdfbf4'
GOLDS = ['#8a6a08', '#a67c00', '#b8860b', '#c9a227', '#d4af37', '#e0c268']

# ── marble ground: domain-warped fBm veins ─────────────────────────────────
N = 900
lin = np.linspace(-3, 3, N)
X, Y = np.meshgrid(lin, lin)


def fbm(x, y, octaves=5, seed=0):
    r = np.random.default_rng(seed)
    v = np.zeros_like(x)
    amp, freq = 1.0, 0.55
    for _ in range(octaves):
        px, py = r.uniform(0, 100, 2)
        v += amp * np.sin(freq * (x + px) + 1.7 * np.cos(freq * (y + py)))
        v += amp * np.cos(freq * (y + py) - 1.3 * np.sin(freq * (x + px) * 0.7))
        amp *= 0.55
        freq *= 1.9
    return v


warp = fbm(X, Y, 4, seed=11)
veins = fbm(X + 0.4 * warp, Y + 0.4 * warp, 5, seed=23)
marble = np.abs(np.sin(1.1 * veins))
marble_cmap = LinearSegmentedColormap.from_list(
    'marble', [(0.0, '#ece2cc'), (0.45, '#f8f4e8'), (0.8, '#ffffff'), (1.0, '#efe6d2')]
)

# ── the dynamical system: spiral sink + off-centre secondary vortex ────────
def flow(x, y):
    # primary: gentle spiral sink at origin (no limit cycle → no pile-up)
    u = -y - 0.16 * x
    v = x - 0.16 * y
    # secondary influence: soft vortex up-right
    dx, dy = x - 1.15, y - 0.85
    d2 = dx * dx + dy * dy + 0.4
    u += 0.9 * dy / d2
    v += -0.9 * dx / d2
    return u, v


def rk4_path(p, h=0.02, steps=340):
    pts = [p]
    x, y = p
    for _ in range(steps):
        k1 = flow(x, y)
        k2 = flow(x + h / 2 * k1[0], y + h / 2 * k1[1])
        k3 = flow(x + h / 2 * k2[0], y + h / 2 * k2[1])
        k4 = flow(x + h * k3[0], y + h * k3[1])
        x += h / 6 * (k1[0] + 2 * k2[0] + 2 * k3[0] + k4[0])
        y += h / 6 * (k1[1] + 2 * k2[1] + 2 * k3[1] + k4[1])
        pts.append((x, y))
        if x * x + y * y < 0.004:
            break
    return np.array(pts)


# ── figure ─────────────────────────────────────────────────────────────────
fig = plt.figure(figsize=(8.5, 8.5), dpi=72)  # 612pt like the siblings
ax = fig.add_axes([0, 0, 1, 1])
ax.set_xlim(-3, 3)
ax.set_ylim(-3, 3)
ax.set_aspect('equal')
ax.axis('off')

def clipped(artist):
    artist.set_clip_path(plt.Circle((0, 0), 3.0, transform=ax.transData))
    return artist

# marble ground
clipped(ax.imshow(marble, extent=[-3, 3, -3, 3], cmap=marble_cmap,
                  origin='lower', interpolation='bilinear', zorder=0))

# faint gold veining on the strongest ridges
vein = np.where(marble > 0.88, marble, np.nan)
clipped(ax.imshow(vein, extent=[-3, 3, -3, 3], origin='lower',
                  cmap=LinearSegmentedColormap.from_list('gv', ['#00000000', '#b8860b30']),
                  interpolation='bilinear', zorder=1))

# ── golden trajectories: two rings of seeds + a few strays ─────────────────
seeds = []
for r, n, jit in [(2.85, 26, 0.05), (2.1, 14, 0.12)]:
    for th in np.linspace(0, 2 * np.pi, n, endpoint=False):
        th2 = th + rng.uniform(-jit, jit)
        seeds.append((r * np.cos(th2), r * np.sin(th2)))
seeds += [(rng.uniform(-1.6, 1.9), rng.uniform(-1.6, 1.9)) for _ in range(8)]

gold_cmap = LinearSegmentedColormap.from_list('golds', GOLDS)
for i, s in enumerate(seeds):
    path = rk4_path(s, steps=rng.integers(220, 400))
    if len(path) < 8:
        continue
    segs = np.stack([path[:-1], path[1:]], axis=1)
    t = np.linspace(0, 1, len(segs))                    # 0 = tail, 1 = head
    base = to_rgb(gold_cmap(rng.uniform(0.15, 0.95)))
    colors = np.zeros((len(segs), 4))
    colors[:, :3] = base
    colors[:, 3] = 0.16 + 0.6 * t**1.3                  # fade in toward the sink
    lc = LineCollection(segs, colors=colors,
                        linewidths=0.5 + 1.5 * t**1.6,  # taper thin → full
                        capstyle='round', zorder=3)
    clipped(ax.add_collection(lc))

# centre: the site's curved-diamond ✦ where all influence collects
from matplotlib.path import Path as MPath
from matplotlib.patches import PathPatch

def curved_diamond(cx, cy, r, waist=0.30):
    """Four-pointed star with concave bezier edges (the ✦ mark)."""
    tips = [(cx, cy + r), (cx + r, cy), (cx, cy - r), (cx - r, cy)]
    verts, codes = [tips[0]], [MPath.MOVETO]
    for i in range(4):
        a, b = tips[i], tips[(i + 1) % 4]
        mx, my = (a[0] + b[0]) / 2, (a[1] + b[1]) / 2
        ctrl = (cx + (mx - cx) * waist, cy + (my - cy) * waist)  # pulled to centre
        verts += [ctrl, b]
        codes += [MPath.CURVE3, MPath.CURVE3]
    return MPath(verts, codes)

star = curved_diamond(0.0, 0.0, 0.34)
ax.add_patch(PathPatch(star, fc='#b8860b', ec='#8a6a08', lw=0.8,
                       zorder=4, joinstyle='round'))

# ── matte orb shading: limb darkening + broad milky key, no gloss ──────────
rr = np.clip(np.sqrt(X**2 + Y**2) / 3.0, 0, 1)
shade = np.clip(np.sqrt(1 - rr**2) ** 0.6, 0, 1)        # 1 centre → 0 rim
key = np.exp(-(((X + 1.35) ** 2 + (Y - 1.5) ** 2) / 7.0))

dark = np.zeros((N, N, 4))
dark[..., 0:3] = np.array([0.20, 0.16, 0.09])
dark[..., 3] = (1 - shade) ** 1.15 * 0.62
clipped(ax.imshow(dark, extent=[-3, 3, -3, 3], origin='lower',
                  interpolation='bilinear', zorder=5))

milk = np.zeros((N, N, 4))
milk[..., 0:3] = 1.0
milk[..., 3] = key * shade * 0.38
clipped(ax.imshow(milk, extent=[-3, 3, -3, 3], origin='lower',
                  interpolation='bilinear', zorder=6))

# hairline gold rim
ax.add_patch(plt.Circle((0, 0), 2.985, fill=False, ec='#a67c00',
                        lw=1.6, alpha=0.9, zorder=7))

fig.savefig('icon.svg', transparent=True)
fig.savefig('preview.png', transparent=True, dpi=150)
print('wrote icon.svg + preview.png')