hologram_visualizations - zfifteen/unified-framework GitHub Wiki
This document provides comprehensive examples and documentation for the enhanced hologram.py module, which supports advanced geometric visualizations relevant to the Z framework.
The enhanced hologram visualization system provides:
- Modular Architecture: Class-based design with configurable parameters
- Advanced Visualizations: Enhanced logarithmic spirals, Gaussian prime spirals, modular tori, and 5D projections
- Interactive Exploration: Parameter variation and batch generation capabilities
- Z Framework Integration: Uses golden ratio transforms and 5D helical embeddings
- Comprehensive Documentation: Full API documentation and examples
- Configurable spiral rates and height scaling methods
- Support for 2D and 3D projections
- Prime highlighting with customizable colors and markers
- Multiple angle increment schemes (golden ratio, π-based, custom)
- Optional connection lines between prime points
- Helical coordinate mapping
- Configurable modular bases and torus parameters
- Residue class filtering and coloring
- Wireframe torus visualization
- Helical embeddings using Z framework transforms
- Multiple projection types (helical, orthogonal, perspective)
- Geodesic line visualization between primes
- Batch generation with parameter variations
- Automated file saving and organization
- Statistical analysis and reporting
from hologram import AdvancedHologramVisualizer
# Create visualizer with 1000 data points
visualizer = AdvancedHologramVisualizer(n_points=1000)
# Generate all visualizations and save to files
visualizer.visualize_all(save_plots=True, output_dir="./visualizations")
# Get statistics about the data
stats = visualizer.get_statistics()
print(f"Generated {stats['prime_count']} primes out of {stats['n_points']} points")from hologram import AdvancedHologramVisualizer
# Initialize with custom parameters
visualizer = AdvancedHologramVisualizer(
n_points=2000,
helix_freq=0.15,
use_log_scale=True,
figure_size=(14, 10)
)
# Create basic 3D prime geometry visualization
fig = visualizer.prime_geometry_3d(save_path="prime_geometry.png")# Different spiral configurations
spiral_configs = [
{
'spiral_rate': 0.1,
'height_scale': 'sqrt',
'projection': '3d'
},
{
'spiral_rate': 0.2,
'height_scale': 'log',
'projection': '3d'
},
{
'spiral_rate': 0.05,
'height_scale': 'linear',
'projection': '2d'
}
]
for i, config in enumerate(spiral_configs):
fig = visualizer.logarithmic_spiral(
**config,
save_path=f"spiral_{i+1}.png"
)# Golden ratio angle increments (recommended)
fig1 = visualizer.gaussian_prime_spiral(
angle_increment='golden',
connection_lines=True,
save_path="gaussian_golden.png"
)
# π-based angle increments
fig2 = visualizer.gaussian_prime_spiral(
angle_increment='pi',
connection_lines=False,
save_path="gaussian_pi.png"
)
# Custom angle increments
fig3 = visualizer.gaussian_prime_spiral(
angle_increment='custom',
connection_lines=True,
save_path="gaussian_custom.png"
)# Different modular bases and torus parameters
torus_configs = [
{
'mod1': 17,
'mod2': 23,
'torus_ratio': 3.0,
'residue_filter': 6
},
{
'mod1': 11,
'mod2': 13,
'torus_ratio': 2.5,
'residue_filter': 4
},
{
'mod1': 7,
'mod2': 19,
'torus_ratio': 4.0,
'residue_filter': 8
}
]
for i, config in enumerate(torus_configs):
fig = visualizer.modular_torus(
**config,
save_path=f"torus_{i+1}.png"
)# Different 5D projection types
projection_configs = [
{
'projection_type': 'helical',
'dimensions': (0, 1, 2) # x, y, z coordinates
},
{
'projection_type': 'orthogonal',
'dimensions': (1, 2, 3) # y, z, w coordinates
},
{
'projection_type': 'perspective',
'dimensions': (0, 2, 4) # x, z, u coordinates
}
]
for i, config in enumerate(projection_configs):
fig = visualizer.projection_5d(
**config,
save_path=f"projection_5d_{i+1}.png"
)# Enhanced zeta landscape with custom parameters
fig = visualizer.riemann_zeta_landscape(
real_range=(0.1, 1.0),
imag_range=(10, 100),
resolution=150,
save_path="zeta_landscape.png"
)# Run comprehensive exploration with multiple parameter sets
visualizer.interactive_exploration(
save_plots=True,
output_dir="./comprehensive_analysis"
)
# Get detailed statistics
stats = visualizer.get_statistics()
print("Analysis Statistics:")
print(f"- Data points: {stats['n_points']}")
print(f"- Prime count: {stats['prime_count']}")
print(f"- Prime density: {stats['prime_density']:.4f}")
print(f"- Helix frequency: {stats['helix_frequency']}")
if stats['embedding_statistics']:
print("5D Embedding Statistics:")
print(f"- Mean coordinates: {stats['embedding_statistics']['mean']}")
print(f"- Std deviation: {stats['embedding_statistics']['std']}")# Customize visualization appearance
visualizer = AdvancedHologramVisualizer(n_points=5000)
# Modify color scheme
visualizer.prime_color = 'gold'
visualizer.prime_marker = '^'
visualizer.prime_size = 75
visualizer.nonprime_color = 'darkblue'
visualizer.nonprime_alpha = 0.4
# Generate visualization with custom colors
fig = visualizer.prime_geometry_3d()# Use with Z framework core modules (when available)
try:
from core.domain import UniversalZetaShift
from core.axioms import universal_invariance
# Create custom zeta shifts for specific analysis
zeta_shift = UniversalZetaShift(10, 20, 30)
z_value = zeta_shift.compute_z()
# Integrate with hologram visualizations
visualizer = AdvancedHologramVisualizer(n_points=1000)
fig = visualizer.projection_5d(projection_type='helical')
except ImportError:
print("Core Z framework modules not available - using local implementations")# Analyze different scales and parameters
scales = [500, 1000, 2000, 5000]
results = {}
for scale in scales:
visualizer = AdvancedHologramVisualizer(n_points=scale)
stats = visualizer.get_statistics()
results[scale] = stats
# Generate scaled visualizations
output_dir = f"./analysis_scale_{scale}"
visualizer.interactive_exploration(save_plots=True, output_dir=output_dir)
# Compare results across scales
for scale, stats in results.items():
print(f"Scale {scale}: {stats['prime_density']:.4f} prime density")-
n_points(int): Number of data points to generate (default: 5000) -
helix_freq(float): Frequency for helical coordinates (default: 0.1003033) -
use_log_scale(bool): Use logarithmic scaling for y-axis (default: False) -
figure_size(tuple): Size for matplotlib figures (default: (12, 8))
Create 3D prime geometry visualization with ZetaShift transforms.
Enhanced logarithmic spiral with configurable parameters.
-
spiral_rate: Rate of spiral growth -
height_scale: Height scaling method ('sqrt', 'log', 'linear') -
projection: Projection type ('3d', '2d')
Gaussian prime spirals with configurable angle increments.
-
angle_increment: Angle increment type ('golden', 'pi', 'custom') -
connection_lines: Whether to draw lines between primes
Modular torus visualization with configurable parameters.
-
mod1,mod2: Modular bases -
torus_ratio: Ratio of minor to major radius -
residue_filter: Residue class filter
5D projections using helical embeddings from Z framework.
-
projection_type: Type of projection ('helical', 'orthogonal', 'perspective') -
dimensions: Which 3 dimensions to project
Enhanced Riemann zeta landscape visualization.
Interactive exploration of all visualization types with parameter variations.
Get statistical information about computed data including prime counts, density, and 5D embedding statistics.
The visualizations use golden ratio curvature transformations:
θ'(n,k) = φ·((n mod φ)/φ)^k
where φ ≈ 1.618 is the golden ratio and k is the curvature parameter.
Points are embedded in 5D space using:
- x = √n · cos(θ_D)
- y = √n · sin(θ_E)
- z = Z/(e²) (frame normalized)
- w = log(n+1) (invariant dimension)
- u = n/c (relativistic dimension)
The system integrates with the Z framework's universal form Z = A(B/c) where:
- A is frame-dependent quantity
- B is rate
- c is the universal invariant (speed of light)
- For large datasets (n_points > 10,000), some visualizations may take several minutes
- 5D projections are computationally intensive and recommended for n_points < 5,000
- File saving adds overhead but enables batch analysis
- Memory usage scales approximately O(n_points) for most visualizations
- Import Errors: Ensure you're running from the correct directory and PYTHONPATH is set
- Memory Issues: Reduce n_points for large visualizations
- Slow Performance: Use smaller datasets for testing, larger for final analysis
- Missing Plots: Check that matplotlib backend is properly configured for your environment
# Set up environment
cd /path/to/unified-framework/src/number-theory/prime-curve
export PYTHONPATH=/path/to/unified-framework
# Install dependencies
pip install numpy matplotlib scipy
# Run basic test
python3 -c "from hologram import AdvancedHologramVisualizer; v = AdvancedHologramVisualizer(100); print('Success!')"This enhanced hologram visualization system provides powerful tools for exploring geometric phenomena in number theory through the lens of the Z framework, enabling both mathematical research and educational visualization.