import numpy as np
from scipy.spatial.distance import pdist
import matplotlib.pyplot as plt
def surpass_openai_zchg(n=10000, seed=42):
"""
Advanced zchg.org Hybrid: Golden Recursive Tower
Aims for extreme local harmonic density via layered φ-spirals,
multiple harmonic rotations, D_n(r) modulation, and power-tower phases.
"""
np.random.seed(seed)
phi = (1 + np.sqrt(5)) / 2.0
points = []
base_scale = 1.0
for layer in range(28): # Deep recursion ("tower height")
m = max(120, int(n / 14) + layer * 65)
t = np.linspace(0, 2 * np.pi * (layer * 1.3 + 8), m)
# D_n(r) + φ-power inspired radial
fib = phi**layer / np.sqrt(5)
radial = base_scale * np.exp(0.42 * t) * (phi ** (-0.78 * layer)) * (2 ** (layer * 0.38))
# Multiple symmetry copies (harmonic rotations)
for rot in range(5):
shift = rot * (2 * np.pi / 5) + layer * phi**0.7
phase_mod = np.sin(layer**1.6 * phi) * 0.35
x = radial * np.cos(t + shift + phase_mod)
y = radial * np.sin(t + shift + phase_mod)
points.append(np.column_stack((x, y)))
base_scale *= 0.78 # Contract layers for density overlap
pts = np.vstack(points)[:n]
pts = pts - np.mean(pts, axis=0)
# Normalize aggressively around unit distance
dists = pdist(pts)
scale_factor = np.percentile(dists, 35) * 0.96 # Target rich overlap zone
pts = pts / scale_factor
return pts.astype(np.float32)
def analyze(pts, tol_loose=0.058, tol_tight=0.014):
dists = pdist(pts)
loose = np.sum(np.abs(dists - 1.0) < tol_loose)
tight = np.sum(np.abs(dists - 1.0) < tol_tight)
n = len(pts)
print(f"\n=== zchg Golden Recursive Tower Surpass Run ===")
print(f"n = {n:,}")
print(f"Loose unit-distance pairs (tol={tol_loose}): {loose:,}")
print(f"Tight unit-distance pairs (tol={tol_tight}): {tight:,}")
print(f"Avg loose degree: {2 * loose / n:.2f}")
print(f"Avg tight degree: {2 * tight / n:.2f}")
print(f"u(n) / n (loose): {loose / n:.2f}")
print(f"u(n) / n² ratio (loose): {loose / (n * (n-1) / 2):.5f}")
# Local hotspots
dmat_sample = squareform(dists[:n*200]) if n > 2000 else squareform(dists) # avoid full matrix if large
# (full matrix skipped for memory)
return pts, loose, tight
if __name__ == "__main__":
points = surpass_openai_zchg(n=10000)
points, loose, tight = analyze(points)
# Plot
plt.figure(figsize=(11, 11))
plt.scatter(points[:,0], points[:,1], s=1.2, alpha=0.75, c='deepskyblue')
plt.title('zchg.org Golden Recursive Tower\nHigh Harmonic Unit-Distance Density')
plt.axis('equal')
plt.grid(True, alpha=0.2)
plt.show()
import numpy as np
from scipy.spatial.distance import pdist
import matplotlib.pyplot as plt
def zchg_supreme_tower(n=12000, seed=42):
"""
Supreme zchg.org Golden Recursive Tower
Pushes high harmonic unit-distance density using deep recursion,
multi-fold symmetries, and aggressive D_n(r) + φ-power modulation.
"""
np.random.seed(seed)
phi = (1 + np.sqrt(5)) / 2.0
points = []
for layer in range(35): # Deep "class field tower" proxy
m = max(90, int(n * 0.085) + layer * 95)
t = np.linspace(0, 2 * np.pi * (layer * 1.618034 + 7), m)
# Enhanced D_n(r) operator
fib = phi**layer / np.sqrt(5)
r_base = np.sqrt(phi * fib * (2 ** (layer * 0.48)) * 1.72)
radial = r_base * (phi ** (-0.71 * layer)) * np.exp(0.338 * t)
# Multiple harmonic symmetries
for sym in range(7):
shift = sym * (2 * np.pi / 6.8) + layer * phi**0.6
phase = np.sin(layer**1.35 * phi) * 0.48 + np.cos(t * 1.25) * 0.12
x = radial * np.cos(t + shift + phase)
y = radial * np.sin(t + shift + phase)
points.append(np.column_stack((x, y)))
pts = np.vstack(points)[:n]
pts = pts - np.mean(pts, axis=0)
# Normalize to rich unit-distance regime
dists = pdist(pts)
scale = np.percentile(dists[(dists > 0.005) & (dists < 50)], 26)
pts = pts / (scale * 0.93)
return pts
def analyze(pts, tol_loose=0.058, tol_tight=0.015):
dists = pdist(pts)
n = len(pts)
loose_pairs = np.sum(np.abs(dists - 1.0) < tol_loose)
tight_pairs = np.sum(np.abs(dists - 1.0) < tol_tight)
print(f"\n=== zchg Supreme Golden Recursive Tower ===")
print(f"n = {n:,}")
print(f"Loose unit pairs (tol={tol_loose}): {loose_pairs:,}")
print(f"Tight unit pairs (tol={tol_tight}): {tight_pairs:,}")
print(f"Avg loose degree: {2 * loose_pairs / n:.2f}")
print(f"Avg tight degree: {2 * tight_pairs / n:.2f}")
print(f"u(n)/n (loose): {loose_pairs / n:.2f}")
return pts
if __name__ == "__main__":
points = zchg_supreme_tower(n=12000) # Increase n as desired
points = analyze(points)
# Plot with density coloring (optional - comment out if slow)
plt.figure(figsize=(12, 12))
plt.scatter(points[:,0], points[:,1], s=1.0, alpha=0.75, c='gold', edgecolors='none')
plt.title('zchg Supreme Golden Recursive Tower\nHigh-Density Harmonic Unit Distances')
plt.axis('equal')
plt.grid(True, alpha=0.2)
plt.show()
import numpy as np
from scipy.spatial.distance import pdist
import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation
def zchg_ultra_tower(n=15000, seed=42):
"""Ultra-pushed zchg.org Golden Recursive Tower"""
np.random.seed(seed)
phi = (1 + np.sqrt(5)) / 2.0
accum = []
frames = [] # For animation (cumulative snapshots)
for layer in range(45): # Very deep tower
m = max(130, int(n * 0.088) + layer * 95)
t = np.linspace(0, 2 * np.pi * (layer * 1.618034 + 7.8), m)
# Aggressive D_n(r) + power tower modulation
fib = phi**layer / np.sqrt(5)
r_base = np.sqrt(phi * fib * (2 ** (layer * 0.51)) * 1.82)
radial = r_base * (phi ** (-0.685 * layer)) * np.exp(0.333 * t)
for sym in range(7):
shift = sym * (2 * np.pi / 6.4) + layer * phi**0.59
phase = np.sin(layer**1.38 * phi) * 0.49 + np.cos(t * 1.28) * 0.155
x = radial * np.cos(t + shift + phase)
y = radial * np.sin(t + shift + phase)
accum.append(np.column_stack((x, y)))
# Take animation snapshot periodically
if (layer * 7 + sym) % 5 == 0 and len(np.concatenate(accum)) >= 4000:
current = np.vstack(accum)[:n]
frames.append(current.copy())
pts = np.vstack(accum)[:n]
pts = pts - np.mean(pts, axis=0)
# Normalize to ultra-rich unit distance regime
dists = pdist(pts)
scale = np.percentile(dists[(dists > 0.008) & (dists < 50)], 20)
pts = pts / (scale * 0.895)
return pts, frames
def analyze(pts):
dists = pdist(pts)
n = len(pts)
loose = np.sum(np.abs(dists - 1.0) < 0.055)
tight = np.sum(np.abs(dists - 1.0) < 0.0135)
print(f"\n=== zchg ULTRA Golden Recursive Tower (Pushed Hard) ===")
print(f"n = {n:,}")
print(f"Loose unit pairs (tol=0.055): {loose:,} → Avg degree: {2*loose/n:.2f}")
print(f"Tight unit pairs (tol=0.0135): {tight:,} → Avg degree: {2*tight/n:.2f}")
return pts
# ============== RUN ==============
if __name__ == "__main__":
points, anim_frames = zchg_ultra_tower(n=15000)
points = analyze(points)
# ============== LIVE ANIMATION ==============
fig, ax = plt.subplots(figsize=(11, 11))
ax.set_xlim(points[:,0].min()*1.1, points[:,0].max()*1.1)
ax.set_ylim(points[:,1].min()*1.1, points[:,1].max()*1.1)
scatter = ax.scatter([], [], s=1.2, alpha=0.8, c='gold')
ax.set_title('zchg ULTRA Golden Recursive Tower Building...\nLayer by Layer', fontsize=14)
ax.axis('equal')
ax.grid(True, alpha=0.2)
def animate(i):
current = anim_frames[min(i, len(anim_frames)-1)]
scatter.set_offsets(current)
ax.set_title(f'zchg ULTRA Golden Recursive Tower\nLayer {i+1}/{len(anim_frames)} | n={len(current):,}')
return scatter,
ani = FuncAnimation(fig, animate, frames=len(anim_frames), interval=120, repeat=True)
plt.show()
import numpy as np
from scipy.spatial.distance import pdist
import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation
def zchg_ultra_tower(n=15000, seed=42):
np.random.seed(seed)
phi = (1 + np.sqrt(5)) / 2.0
accum = []
frames = []
for layer in range(45):
m = max(130, int(n * 0.088) + layer * 95)
t = np.linspace(0, 2 * np.pi * (layer * 1.618034 + 7.8), m)
fib = phi**layer / np.sqrt(5)
r_base = np.sqrt(phi * fib * (2 ** (layer * 0.51)) * 1.82)
radial = r_base * (phi ** (-0.685 * layer)) * np.exp(0.333 * t)
for sym in range(7):
shift = sym * (2 * np.pi / 6.4) + layer * phi**0.59
phase = np.sin(layer**1.38 * phi) * 0.49 + np.cos(t * 1.28) * 0.155
x = radial * np.cos(t + shift + phase)
y = radial * np.sin(t + shift + phase)
accum.append(np.column_stack((x, y)))
if (layer * 7 + sym) % 6 == 0:
current = np.vstack(accum)[:n]
frames.append(current.copy())
pts = np.vstack(accum)[:n]
pts = pts - np.mean(pts, axis=0)
dists = pdist(pts)
scale = np.percentile(dists[(dists > 0.008) & (dists < 50)], 20)
pts = pts / (scale * 0.895)
return pts, frames
def analyze(pts):
dists = pdist(pts)
n = len(pts)
loose = np.sum(np.abs(dists - 1.0) < 0.055)
tight = np.sum(np.abs(dists - 1.0) < 0.0135)
print(f"\n=== zchg ULTRA Golden Recursive Tower ===")
print(f"n = {n:,}")
print(f"Loose unit pairs (tol=0.055): {loose:,} → Avg degree: {2*loose/n:.2f}")
print(f"Tight unit pairs (tol=0.0135): {tight:,} → Avg degree: {2*tight/n:.2f}")
return pts
if __name__ == "__main__":
points, anim_frames = zchg_ultra_tower(n=15000)
points = analyze(points)
fig, ax = plt.subplots(figsize=(11, 11))
ax.set_xlim(points[:,0].min()*1.1, points[:,0].max()*1.1)
ax.set_ylim(points[:,1].min()*1.1, points[:,1].max()*1.1)
scatter = ax.scatter([], [], s=1.2, alpha=0.8, c='gold')
ax.set_title('zchg ULTRA Golden Recursive Tower Building...', fontsize=14)
ax.axis('equal')
ax.grid(True, alpha=0.2)
def animate(i):
idx = min(i, len(anim_frames)-1)
current = anim_frames[idx]
scatter.set_offsets(current)
ax.set_title(f'zchg ULTRA Golden Recursive Tower\nLayer {idx+1}/{len(anim_frames)} | n={len(current):,}')
return scatter,
ani = FuncAnimation(fig, animate, frames=len(anim_frames), interval=120, repeat=True)
plt.show()
import numpy as np
from scipy.spatial.distance import pdist
import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation
def zchg_ultra_tower(n=20000, seed=42):
np.random.seed(seed)
phi = (1 + np.sqrt(5)) / 2.0
accum = []
frames = []
for layer in range(52):
m = max(180, int(n * 0.072) + layer * 110)
t = np.linspace(0, 2 * np.pi * (layer * 1.618034 + 9.2), m)
# Strong D_n(r) + φ-power modulation
fib = phi**layer / np.sqrt(5)
r_base = np.sqrt(phi * fib * (2 ** (layer * 0.55)) * 1.95)
radial = r_base * (phi ** (-0.67 * layer)) * np.exp(0.325 * t)
for sym in range(8):
shift = sym * (2 * np.pi / 6.2) + layer * phi**0.62
phase = np.sin(layer**1.42 * phi) * 0.52 + np.cos(t * 1.32) * 0.18
x = radial * np.cos(t + shift + phase)
y = radial * np.sin(t + shift + phase)
accum.append(np.column_stack((x, y)))
if (layer * 8 + sym) % 7 == 0:
current = np.vstack(accum)[:n]
frames.append(current.copy())
pts = np.vstack(accum)[:n]
pts = pts - np.mean(pts, axis=0)
# Normalize for maximum unit distance overlap
dists = pdist(pts)
scale = np.percentile(dists[(dists > 0.01) & (dists < 60)], 18)
pts = pts / (scale * 0.88)
return pts, frames
def analyze(pts):
dists = pdist(pts)
n = len(pts)
loose = np.sum(np.abs(dists - 1.0) < 0.052)
tight = np.sum(np.abs(dists - 1.0) < 0.013)
print(f"\n=== zchg ULTRA Golden Recursive Tower (n={n:,}) ===")
print(f"Loose unit pairs (tol=0.052): {loose:,}")
print(f"Tight unit pairs (tol=0.013): {tight:,}")
print(f"Avg loose degree: {2*loose/n:.2f}")
print(f"Avg tight degree: {2*tight/n:.2f}")
return pts
if __name__ == "__main__":
points, anim_frames = zchg_ultra_tower(n=20000)
points = analyze(points)
# ============== ANIMATION ==============
fig, ax = plt.subplots(figsize=(12, 12))
ax.set_xlim(points[:,0].min()*1.15, points[:,0].max()*1.15)
ax.set_ylim(points[:,1].min()*1.15, points[:,1].max()*1.15)
scatter = ax.scatter([], [], s=0.9, alpha=0.85, c='gold')
ax.set_title('zchg ULTRA Golden Recursive Tower - Building...', fontsize=15)
ax.axis('equal')
ax.grid(True, alpha=0.25)
def animate(i):
idx = min(i, len(anim_frames)-1)
current = anim_frames[idx]
scatter.set_offsets(current)
ax.set_title(f'zchg ULTRA Golden Recursive Tower\nLayer {idx+1}/{len(anim_frames)} | n={len(current):,}')
return scatter,
ani = FuncAnimation(fig, animate, frames=len(anim_frames), interval=80, repeat=True)
plt.show()
