Visual Assets

Visual Assets#

Gallery of all visual and interactive resources across the framework, organized by type.

Application	Description
Stern-Brocot Walk	Navigate the Stern-Brocot tree interactively. Explore mediant construction, Farey neighbors, and the rational hierarchy.
Ontology Viewer	Framework concept map. Visual index of how derivations, primitives, and predictions connect.
Mobius Views	Mobius strip visualizations. The non-orientable topology underlying the two-root structure.
Mobius Projector	Projection tool for Mobius strip geometry.
Our Address	The universe’s computational clock. Stern-Brocot coordinates, progress, and predictions.
Intersections	Stick-slip dynamics with interactive Plotly and Canvas visualizations. Lagrangian relaxation, Stribeck curves, and bifurcation thresholds.
Stribeck Optics	Optical friction visualization. Stribeck curve mapped to refractive phenomena.
First Principles	sin(ωt) to Einstein. The complete derivation in 10 steps, with an evolving waveform background.
Oscillations	47 oscillations of f(x) = 1/(1+x). Pipes screensaver, Fibonacci sequence, pure math of 1/φ.
Derivation Graph	Interactive D3 force-directed graph of the framework’s derivation chain and repository structure.

File	Description
stairs.gif	Devil’s staircase construction. Tongues filling the frequency axis as coupling increases.
triangles.gif	Stern-Brocot tree triangulation. Mediant insertion building the rational hierarchy.
orbit.gif	Circle map orbit. Phase evolution showing mode-locking and quasiperiodicity.
spiral.gif	Spiral convergence. Floquet decay inside an Arnold tongue.
rose.gif	Rose curve from rational frequency ratios. Winding number geometry on the circle.

File	Description
minimum_self_predicting_universe.svg	The minimum self-predicting universe. Schematic of the four-primitive alphabet and its compositions.
staircase_forming.svg	Staircase formation. How Arnold tongues fill the frequency axis at increasing coupling.

Phase portraits from the original Kuramoto-Einstein mapping.

File	Description
phase_newtonian.png	Phase portrait: Newtonian regime (\(g \gg a_0\)). Decoupled orbits.
phase_mond.png	Phase portrait: MOND regime (\(g \ll a_0\)). Entrained orbits.
phase_transition.png	Phase portrait: transition regime (\(g \approx a_0\)). The synchronization boundary.

Computational outputs from the derivation scripts.

Script source	Content
`circle_map.py`	Arnold tongues, devil’s staircase at varying \(K\)
`golden_ratio_pivot.py`	Zoom into \(1/\varphi\), identifying the pivot scale
`phi_squared_zoom.py`	Exact \(\varphi^2\) self-similarity at the golden ratio
`k_omega_mapping.py`	The \(k \leftrightarrow \Omega\) mapping: spectral tilt rate and amplitude
`staircase_geometry.py`	3D representations: Arnold surface, Poincare disk, curvature
`born_rule_tongues.py`	Tongue boundary geometry confirming \(\Delta\theta \propto \sqrt{\varepsilon}\)
`collapse_tongues.py`	Floquet convergence rate and collapse duration
`fidelity_calibration.py`	RAR interpolating function from tongue self-consistency
`a0_high_z.py`	High-redshift \(a_0(z)\) predictions and observational comparison

All scripts are in the harmonics/sync_cost/derivations directory.