FLOW: One State, Two Futures

The easiest way to make two simulations look different is to start them differently. The easiest way to miss that mistake is to put the pictures next to each other and call the arrangement a comparison.

FLOW's central operation is therefore a copy before it is a change.

Copy the state, not the appearance

A dye image is not the whole fluid state. Two frames can show the same concentration while carrying different velocity fields. They may also carry different continuation buffers, clocks or input histories. Copying only the visible texture would make a persuasive visual match and a poor experimental control.

The internal comparison contract copies the full relevant numerical state at one committed tick. Both chambers then evolve under a shared clock. The intervention changes B's viscosity; it does not also change the initial dye, the camera, the input or the observation time.

The article below presents recorded scalar measurements from one named run. It does not run the solver in your browser or turn a historical recording into a new live experiment.

Keep the times matched and move through the stored samples. Then deliberately break the match. A is now observed at one time and B at another. Even if both energy values are accurately reported, their difference no longer isolates the viscosity intervention.

Use Compare different model times to introduce the confound, then Restore matched model time to remove it. Read the actual A/B times beside the bars: the difference isolates the intended viscosity intervention only when those observation times match.

Equality is the first experiment

Before asking whether different viscosities produce a difference, ask whether identical copies with identical parameters stay identical. This is the null experiment. It catches errors that an exciting positive result can hide: stale buffers, inconsistent stepping, external input reaching one branch, or a fork taken at two slightly different times.

On the tested device and implementation, FLOW's exact-copy and input-replay checks compare raw fields, not screenshots. Bit-identical continuation is a useful software contract within that scope. It is not a promise that every browser or GPU produces the same floating-point result.

The distinction is practical. A local replay can reproduce an input history on the tested backend. A public setup link has a narrower job: it describes an initial configuration. It does not contain the gesture history, and the public recorded preview does not execute that history.

A difference needs a definition

The explorer reports B minus A for mean kinetic energy. It does not subtract two colors. A signed field difference would answer a different question at each location. A scalar energy difference compresses the whole field into one number.

Neither representation is automatically superior. The useful choice depends on the question. A scalar can reveal a systematic effect; it can also hide where the effect occurs. A field can reveal structure; its color range can also magnify tiny differences until they look dramatic.

Before interpreting a subtraction, name the quantities, units, sign convention and shared time. Keep the scale visible. A bright difference plot whose range is unknown is an invitation to overinterpret.

The measurement has a passport

Open the measurement record under the figure. It identifies the initial field, resolution, timestep, viscosities, diffusivity, method version and separately labeled evidence-report and numerical-source hashes. Downloading the compact records makes the displayed values inspectable without requiring access to the author's workstation.

These details do not certify every possible input. They establish which experiment a sentence refers to. The difference between a useful measurement and a floating claim is often just that connection.

The public swirl guide is attached to a fixed recording. Read its actual A/B labels and matched time. Do not assume a selected guide has produced a new pair of simulations.

The fair comparison is mostly restraint: one copied state, one clock, one intervention, and a control that is allowed to fail.

Next: how one field can be fast without rotating locally.