Spatial Octahedral Quantum Wave Functions

Provides mathematical tools for simulating and visualizing three-dimensional octahedral quantum wave interferences and spatial resonance fields. Includes functions for MRI slice generation of fullerene structures and wave models. Computational modeling and three-dimensional visualization of fullerene and octahedral topologies are implemented within the R statistical environment, with interactive plotting powered by 'plotly'. Theoretical foundations are based on the topological frameworks of Cataldo et al. (2015) , Dresselhaus et al. (1996, ISBN:9780122218200), and Coxeter (1973, ISBN:9780486614809); the geometric principles of equations of the octahedron type are outlined in Bobenko and Suris (2012) . Additional structural and biological symmetry contexts are derived from Bragg (1914) and Caspar and Klug (1962) .

octawave: Dynamic 3D Quantum Waves

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|   o c t a w a v e                                     |
|   >> Multidimensional Wave & Scalar Field Computing   |
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|   Core Developer: Katharina Maria Brecht (2026)       |
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This project simulates dynamic, time-dependent quantum wave fields based on an octahedral structure.

The Origin / Der Ursprung

This system was born from a vivid night-time dream about geometric structures, waves, and collapsing spaces. It is the transition of sub-conscious creative energy into real, working mathematical R code.

License & Academic Identity / Schutz & Akademische Identität

Copyright (C) 2026 Katharina M. Brecht.
ORCID iD: https://orcid.org/0009-0001-2176-7476

Protected under the GNU General Public License v3 (GPL-3.0).
Anyone using or modifying this code MUST credit Katharina M. Brecht (ORCID: 0009-0001-2176-7476) as the original author.

Research Abstract & Core Objectives

The 'octawave' package transcends traditional, static modeling constraints by introducing an applicable framework for three-dimensional (3D) quantum geometry visualization within the R statistical environment.

• Physical Assertion: Quantum waves and resonance fields are inherently dynamic, spatial geometries defined by complex multi-dimensional symmetries (such as octahedral vertex networks).
• Methodology: Through the application of virtual Magnetic Resonance Imaging (MRI) slicing techniques, this framework transforms highly complex mathematical equations into dynamic, interactive, and visually tangible spacetime models.
• Open Science Impact: By providing full reproducibility via open-source R code, this project democratizes advanced quantum geometry—proving that complex spatial interferences can be fully simulated, visualized, and examined on any standard system globally.

Package Features & Functionalities

1. Core Computations

• Scaling of the Quantum Core: Computes the exact 3D coordinates of the six octahedral vertices in space based on their distance from the origin.
• Novel Octahedral Quantum Wave with Spatial Damping: Computes the superposition of waves radiated from the six vertices of an octahedron, integrating quantum-mechanical amplitude damping.
• Time-dependent Octahedron Quantum Wave: Calculates the wave field at an exact time step 't' to simulate dynamic movements and quantum state progressions.

2. Virtual Slicing & Grids

• Pentagon-Hexagon Wave Slice: Scans a complex 5- and 6-edged quantum grid layer by layer, featuring built-in bilingual support.
• Octawave Wave Slice: Scans Katharina's original 6-cornered octawave geometry layer by layer using virtual slicing.
• Export Full Wave Slice Series: Exports a complete series of Fullerene and OCTAWAVE MRI slices as high-resolution PNGs and PDFs.

3. Graphics & UX

• Visualization of the Octawave Quantum Field: Generates an automated, publication-quality 2D cross-section through the octahedral wave field in classic MATLAB aesthetics.
• Interactive 3D Visualization of the Octahedral Wave: Generates a three-dimensional, interactive volume model of the quantum field for real-time exploration via 'plotly'.
• Floating 3D Octawave Visualizer: Plots the quantum wave field at a fixed time step, rendering it as a stunning, continuous 3D landscape.
• Export 3D Octawave Snapshot Series: Saves a sequential series of 3D snapshots as PNG files to capture and visualize continuous wave progression.
• Interactive Drop Zone: Allows users to click directly into the plot to trigger and seed a new wave at that exact physical coordinate.
• Interactive Multi-Drop 3D Zone: Allows users to click three sequential times to dynamically create and overlay overlapping waves within the 3D landscape.

4. Advanced Spectral Analysis & WebGL Acceleration (New in v0.1.1)

• Core Spectral Analysis (wave2lyze): Processes multidimensional spatial coordinates to extract Euclidean amplitudes and applies Fast Fourier Transforms (FFT) to decode hidden quantum interference patterns.
• Topological WebGL Interface (prep_sync3d): Bridges the analytical results of octawave with the 'sync3d' engine. It auto-generates localized node-edge structures for high-performance, frame-accurate 3D rendering, completely bypassing standard browser lag.

Advanced Feature: Quantum Wave Analysis & sync3d Integration

The latest update introduces wave2lyze and prep_sync3d, forming a direct topological bridge to the sync3d package. By transforming spectral analysis data into optimized node-edge matrices, it unlocks high-performance, hardware-accelerated 3D WebGL rendering through the add_synchronized_3d_edges() pipeline without browser lag.

Quick Start: 3D Quantum Wave Synchronization

library(octawave)
library(plotly)
library(sync3d)

# 1. Simulate complex harmonic wave data
time_vec <- seq(0, 4 * pi, length.out = 100)
raw_quantum_data <- data.frame(X = sin(time_vec), Y = cos(time_vec))

# 2. Analyze phase space and generate the topological bridge
analysis <- wave2lyze(raw_quantum_data)
sync_data <- prep_sync3d(analysis)

# 3. Render synchronized structure via the sync3d engine
base_plot <- plot_ly(data = sync_data$nodes, x = ~x, y = ~y, z = ~z,
                     type = 'scatter3d', mode = 'markers',
                     marker = list(size = 4, color = '#008080'))

final_plot <- add_synchronized_3d_edges(base_plot, sync_data$edges)
final_plot

Installation

You can install the official released version of octawave directly from CRAN with:

install.packages("octawave")