OBSERVATION CHAMBER / ACTIVE

OBSERVATION ROUTE

CURRENT: 73 EIKONAL GEODESIC WAVEFRONT OBSERVATORY

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Eikonal Geodesic Wavefront Observatory

Observe arrival time, wavefronts, and fastest paths in a positive speed field with a deterministic eight-neighbour eikonal graph.

field / eikonal wavefront Observation Model

ROUTE 73 / FIELD / EIKONAL WAVEFRONT

ARRIVAL TIME / FASTEST PATH

How a front crosses a positive speed field

A source starts at T(S) = 0. Eight-neighbour travel costs build the arrival-time field T, its level-set wavefront, and a predecessor path to the target.

READY

Select SOURCE or TARGET, then click or drag across the field. The colour is T; WAVEFRONT shows the current level set; PATH shows the predecessor chain.

All calculations stay local in this browser.

medium: UNIFORM
T(G): —
path cost: —
Eikonal RMS: —
finite cells: —
speed range: —
path cells: —
reveal time: τ = 0.000

FIELD CONTROLS

Set the field and front

READY

CHAMBER STATUS

SYSTEM: ONLINE
MODEL: 8-NBHD
FIELD: c > 0

SOLVER

96 × 64 / 6,144

STEP advances the reveal time. PLAY animates it without re-solving. Reduced motion disables PLAY; STEP remains available.

SPEED FIELD

0.5 ≤ c ≤ 1.5

PLACE POINTS

SOURCE

Click or drag on the Canvas. Keys 1/2 select a point; arrows nudge it by one grid cell.

OBSERVATION LENS

T / FRONT / PATH

REVEAL TIME ττ = 0.000

KEYBOARD

Focus the canvas: Space/P PLAY · Enter/S STEP · R RESET · 1/2 point · arrows nudge · Home/End reveal endpoints.

OBSERVATION READOUT

Arrival time and route identity

FINITE

SOURCE cell: —
TARGET cell: —
path cost − T(G): —
Eikonal RMS: —
Eikonal P95: —
predecessor violations: —
observation contract: |∇T| = 1/c, T(S) = 0; graph edge cost uses distance / mean(c)

This is a discrete graph eikonal model. The residual is the Bellman consistency residual for the eight-neighbour arrival field, not a physical-wave measurement.

DETERMINISTIC SELF-TEST

Numerical acceptance

PASS

FIXED FIXTURE / PASS

CHECK	VALUE	LIMIT	RESULT

Observation report

OBSERVATION CONTRACT

Arrival time, not wavelength

The field is a positive static speed c(x,y). T is the accumulated travel time from S. Level sets of T are the wavefront; the predecessor chain is the least-cost graph path to G. There is no frequency, phase, amplitude, dispersion, refraction, radiance, or particle transport.

WHAT TO WATCH

Speed changes route geometry

UNIFORM gives the diagonal-grid approximation to a straight front and route.
GRADIENT changes arrival time across the field while keeping c positive.
SMOOTH WELL slows the centre and bends the least-cost route around it.

MODEL NOTE

Discrete eikonal graph

T(v) = min_u~v [T(u) + d(u,v) / c̄(u,v)]

The fixed grid has 6,144 cells and at most 49,152 directed neighbour checks in total. The solver runs only when the field or points change.

Formula note

|∇T(x,y)| = 1 / c(x,y), T(S) = 0. On the displayed graph, the mean speed on an edge is c̄(u,v) = (c(u) + c(v)) / 2. The discrete residual checks T(v) − min[T(u) + d(u,v)/c̄(u,v)] for every settled non-source cell.

OBSERVATION GUIDE

Touchpoints for observation

Start with UNIFORM and T HEATMAP. Select TARGET and click a new goal, then SOLVE. Switch to WAVEFRONT and use STEP or PLAY to reveal the isochrone.

Compare T(G), PATH COST, and the residual after choosing GRADIENT or SMOOTH WELL.
Use PATH to inspect the predecessor chain. It is a route in the finite grid, not a sampled physical ray.
REPORT makes a local text record and PNG saves the current Canvas. RESET clears the report, state attributes, and ARIA state.

This is a bounded deterministic arrival-time model. It is not a wave simulator, ray tracer, terrain navigator, physical measurement, or visitor tracker.

Runs inside the browser with no upload and no registration.

OBSERVATION POLICY

This chamber runs a deterministic positive speed-field model in your browser. The field, arrival times, path, calculations, reports, and images stay local. It does not measure physical waves, visitors, or terrain.

Route

This chamber belongs to Fields in Motion.

FIELD Back to Fields in Motion Route.