Clock application

Clock

The interactive six-rotor Ptolemaic Clock.

System time
bezel hand
H M S h m s
drive
timing
advance
response
mod
epicycle – – –

Drag any visible hand or bezel. Movement → Drive determines what moves and whether the lane must keep time.

Hour hand + outer bezel Minute hand + middle bezel Second hand + inner bezel

My presets

Import presets

Review the presets in this file before importing them.

    Movement

    Position

    Hand position

    Position sets the visible Hour, Minute, and Second hand poses directly. Default restores the clock's canonical starting pose, 10:10:35 places the three lanes at those independent positions, and Random chooses new hand positions. The readout below reports each lane's physical Hand position, Bezel anchor position, and the Time currently indicated by their relationship.

    Randomization

    Randomization schedules repeated position changes independently for Hour, Minute, and Second. Each lane can be enabled or disabled and assigned an interval in seconds, minutes, or hours. A scheduled change uses the same position-setting mechanism as the Random button and leaves the authored Drive, Epicycle, and Motion settings intact.

    Movement

    Drive

    The shared Hour / Minute / Second selector chooses the lane being edited. Drive defines the target trajectory of each physical Hand and Bezel before any Motion stages are applied.

    Clock

    Clock independently drives that Hand or Bezel at its lane's natural clock rate. Direction is physical CW or CCW; changing direction re-anchors at the current pose so the rotor reverses without jumping.

    Fixed

    Fixed independently holds the rotor at one authored Drive position. Entering Fixed captures the rotor's current pre-Motion position, so leaving Fixed and returning later freezes wherever the rotor has moved to by then. Hour, Minute, Second, and Angle fields are synchronized views of the same fixed position. Motion remains rotor-local after Drive, so an active Motion stage can still move the rendered rotor around a Fixed Drive target.

    Free

    Free independently drives the rotor with an authored speed, direction, and phase. Speed is expressed in the lane's natural revolution period: Hour uses rev/12hr or rev/24hr, Minute uses rev/hr, and Second uses rev/min.

    Coupled

    Coupled independently derives the rotor's Drive from another Hand or Bezel using a ratio, same/opposite direction, and phase. Source choices that would form a circular six-rotor dependency are unavailable. Sync aligns a coupled rotor to its source; Sync coupled and Sync all synchronize larger sets without changing the authored Drive definitions.

    Time slave

    Time slave gives up independent Drive. Its position is dictated by the other element in the same lane so their relative angle indicates the configured time. A lane may have at most one Time slave; with none, Hand and Bezel are independently driven and may still indicate the correct time if their resolved Drives happen to maintain the required relationship. A Time-slave choice that would close a dependency cycle is shown as unavailable and is rejected without changing any existing Drive mode or Coupled source.

    Movement

    Motion

    Motion reshapes each Hand and Bezel locally after Drive has resolved its target. The shared lane selector chooses Hour, Minute, or Second; Hand and Bezel retain independent settings. The four stages are applied in the same order shown in the panel.

    Timing

    Continuous preserves the Drive timebase. Stop-to-go compresses the active travel into the moving part of a cycle and holds at the end, producing a repeated run-and-pause timing pattern.

    Advance

    Smooth passes the Timing trajectory through. Step samples it at a fixed interval. Ratchet quantizes position to angular teeth. Advance therefore controls how the target progresses spatially after Timing.

    Response

    Direct follows the Advance target exactly. Spring makes that target an equilibrium and lets the rotor approach it dynamically; Tension controls stiffness and Bounce controls how much oscillation survives.

    Modulation

    None adds no offset. Pendulum adds a periodic swing with authored amplitude and period. Drift adds a slower periodic displacement. Modulation is the final stage, so it acts on the result of Response.

    Movement

    Epicycle

    Epicycle

    Epicycle moves a bezel's center around the main clock center while that bezel continues to rotate according to Drive and Motion. Radius sets the orbital displacement, Period sets one orbital cycle, and CW / CCW sets orbital direction. The shared Hour / Minute / Second selector follows the same lane selection used by Drive and Motion.

    Path preview

    Path preview draws the recent orbital trace without changing the mechanism. Thickness and Transparency style the trace, while Clock opacity fades the rest of the clock so the epicycle path is easier to inspect. Copy controls can propagate Radius, Period, or the complete epicycle configuration to all three lanes.

    Movement

    Interaction

    Interaction is reserved for defining what a Hand or Bezel should do after direct manipulation ends—for example holding its released pose, snapping to a target, returning toward its authored trajectory, or coasting. These release behaviours are placeholders and do not yet change clock mechanics.

    Clock mechanics

    Mechanics table

    The table is a compact ledger for the six physical rotors. Each rotor is resolved through the same mechanical pipeline: Drive → Timing → Advance → Response → Modulation → Epicycle. Drive establishes the target trajectory; the four Motion stages transform that trajectory locally; Epicycle is the final bezel-center orbit. Applicable table cells are clickable shortcuts to the corresponding Movement editor.

    Columns

    Bezel — H / M / S

    The three uppercase columns describe the Hour, Minute, and Second bezel rotors. Their values are bezel-anchor positions in the natural units of the lane: hours, minutes, or seconds. Epicycle applies only to these bezel columns because it moves the bezel center rather than a hand.

    Hand — h / m / s

    The three lowercase columns describe the corresponding Hour, Minute, and Second hand rotors. A lane tells time through the relationship between its Hand and Bezel. A Time slave guarantees that relationship structurally, but independently driven pairs can also indicate the correct time when their resolved Drive positions happen to agree with wall time.

    Column status

    One 8 px traffic light beside each uppercase H / M / S header measures the corresponding Hand/Bezel pair at the Drive boundary, before Motion or Epicycle. Green means effectively exact wall time, orange means the signed angular error is within the configured Time error ε, and red means the pair is outside ε. ε is defined in Settings as a percentage of one natural lane unit: one hour for Hour, one minute for Minute, and one second for Second. Hover or focus exposes the signed angular error and the current ε threshold. This measured status is independent of whether correctness is guaranteed by a Time slave or emerges from two independent Drives.

    Rows

    Drive

    Drive is the resolved target trajectory before Motion. Authored Drive modes are Clock, Fixed, Free, and Coupled; a Time slave replaces independent authority with the lane-partner relation required to preserve time. The row substitutes Coupled dependencies and Time-slave compensation and simplifies the result, so it shows what each physical rotor is actually being asked to follow rather than the intermediate authored equation. Fixed Drive appears as a constant; coefficients scale rate; a minus sign reverses direction.

    Timing

    Timing changes when the Drive trajectory progresses. Continuous is a pass-through. Stop-to-go, shown as s2g(cycle,hold), compresses travel into the moving portion of a cycle and then pauses. Timing happens before any positional quantization.

    Advance

    Advance changes how the timed target progresses through positions. Smooth is a pass-through, Step samples at a fixed interval, and Ratchet quantizes the target to angular teeth. Because Timing and Advance are separate, combinations such as Stop-to-go + Step remain meaningful.

    Response

    Response controls how the rotor reacts to the Advance target. Direct passes it through. Spring, shown as spr(tension,bounce%), treats each new Advance target as an equilibrium while preserving the rotor's local physical position and velocity, allowing overshoot and ring-down.

    Modulation

    Modulation is applied around the Response trajectory. None is a pass-through. Pendulum adds periodic angular swing, while Drift adds a slower cyclic deviation. These effects remain local to the destination rotor.

    Epicycle

    Epicycle is the final stage and applies only to Bezels. An enabled epicycle moves the bezel center on a circular orbit with authored radius, period, and direction; clockwise notation is ε(r,p) and counterclockwise notation is −ε(r,p). It does not replace the rotor's Drive or Motion rotation.

    Formula mode shows the compact authored/resolved notation. An empty applicable Motion cell means that stage is at its default pass-through setting; an em dash means the stage does not apply. Current values turns the table into a live stage ledger: Drive always reports its current value, while inactive pass-through Motion stages remain blank instead of repeating the value from the row above. Coupled Drive supplies only the destination rotor's Drive target—it never imports the source rotor's Timing, Advance, Response, or Modulation settings—and a Time slave likewise retains its own local Motion after its derived Drive target is resolved.

    Fingerprints

    The Mechanical fingerprint is a deterministic, versioned serialization of movement state. It includes Drive—including Fixed positions—Time-slave, Motion, Epicycle, Position, and related mechanical settings while excluding clock appearance, element visibility, interface theme, fonts, and the diagnostic Time error ε setting. Copy writes the fingerprint in a commented envelope with its mechanical schema version; paste/reload and the validation icon let the field be compared with or applied to the current clock mechanics.

    The Style fingerprint uses the same transport pattern for authored clock appearance only. It deliberately excludes mechanics, bezel order, element visibility, and interface theme/font. A full Current clock JSON export is separate and carries the complete reproducible clock configuration together with both fingerprints for validation.

    Mechanics table

    Drive row

    Drive establishes the resolved target trajectory for each physical rotor before Motion is applied. The table substitutes Coupled dependencies and Time-slave compensation, then simplifies the result, so the row describes what the rotor is actually being asked to follow rather than exposing intermediate equations.

    Clock, Fixed, Free, and Coupled are authored Drive modes. Fixed holds one authored pre-Motion Drive position; Time slave relinquishes independent Drive authority and derives its target from its lane partner so the Hand/Bezel relationship indicates the configured time.