Animation, frames and timing: sources & model

Direct a rigged fox, capture poses and build a real animation. Change pauses, compare in-betweens, inspect a historic motion study, and save your own film.

What supports the explanation?

What this model assumes

1. The fox is a licensed artist-created character, not an anatomical scan or measured animal gait. Its rig bones are animation controls.
2. Placement, easing and timing express an authored performance. No gravity, foot-contact forces, emotion detector or physical mass model is simulated.
3. Our 24-tick timeline and browser rendering opportunities are different. A device can miss frames; callback timing is not a measurement of emitted light.
4. No personal vision test, universal brain frame rate, flicker threshold or prescribed emotional interpretation is inferred.
5. The sampled wheel compares exact ideal angle sets; it does not predict what every viewer will perceive.
6. Source model and historical photographs retain their own identities and credits. Computed in-betweens are authored derivatives.
7. The name: apparent motion: A presentation of changing images can produce perceived motion without the corresponding continuously moving object on the screen. Visual responses do persist over time, but an afterimage alone is not a complete account of directional motion. Adelson and Bergen’s 1985 model describes motion processing through patterns across space and time; our studio does not simulate a brain.
8. Timing and spacing measure different choices: Duration equals total hold ticks divided by 24. Between two pose onsets, represented interval rate equals position change divided by elapsed time. A gap of 20 stage units over 0.25 seconds is 80 units per second; doubling that gap doubles the interval rate. Stage units are authored coordinates, not a fox’s real-world speed.
9. An in-between follows a rule: For scalar placement, linear interpolation gives x = (1−u)x₀ + ux₁. Ease-in/out uses e = 3u²−2u³ in place of u. Rig rotations use normalized quaternion spherical interpolation along a short arc, following glTF rotation semantics. These rules create poses; they do not recover a uniquely true missing observation or enforce foot contact.
10. Output frames are not all new pictures: Eight pictures held for six ticks each make a 48-tick, two-second project. Exporting it at 24 frames per second gives 48 output frames. At 48 frames per second it gives 96. In hold mode those extra frames repeat the same captured states; interpolation is a separate choice.
11. No universal frame rate for seeing: Watson, Ahumada and Farrell’s 1986 experiment asked observers to distinguish sampled motion from a 1920 Hz reference under controlled display and viewing conditions. Its 75%-correct discrimination threshold depended on speed, detail and conditions. Experiment 1 included two observers; it does not prescribe a frame rate for every child, eye or phone. The authors distinguish their visibility theory from a theory of motion sensing.
12. A repeated pattern can hide a turn: Twelve identical spokes repeat their arrangement every 30 degrees. At eight samples per second, a model wheel turning 240 degrees per second advances exactly 30 degrees per sample: its unmarked frames match a stationary wheel. A marked spoke adds identity information. Extra full turns can still hide between samples. This mathematical ambiguity differs from perceptual reversals under continuous input studied by Kline and Eagleman in 2008.
13. Pictures are historical evidence: Muybridge’s 1878 Sallie Gardner plate records different horse positions. Its twelfth panel shows the horse standing. The printed caption claims about 1/25 second between negatives and 1/2000 second exposures: interval and exposure are different quantities. A scan does not establish an exact seamless movie, and the standing reference should not be silently added to a gallop loop.

What has been checked

Analytical reference cases, conservation or transition invariants, finite drawing commands, bounded setup parsing, discovery and route integrity are checked automatically. These checks do not establish anatomical fidelity, learner outcomes or browser/device compatibility. Independent subject review, learner trials, comprehensive accessibility review and browser video encoding checks remain pending.

Each source supports the associated claim. Sources do not certify this implementation or its visuals.

About the cover illustration

A real artist-created Fox rig, original source pose on the Brytalearn stage. PixelMannen model CC0; tomkranis rig/animation and AsoboStudio/scurest conversion CC BY 4.0. Brytalearn lighting, camera and stage.