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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

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")

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.