Method & central finding
The source material: one sliding-block puzzle and ten single-rule variations of it; three alternate win-conditions on the same physics; a headless sweep of 100 procedurally-generated "universes" (movement + interaction + field rules) filtered by automated activity/structure metrics; a second, human-curated version of that same search, bred across generations by direct emoji reaction; a study of permanent world-memory ("Rule Residue"); and ten single-purpose interactive pieces, each built to target one named feeling and each rebuilt two to three times against direct human reaction until it either landed or was retired.
The central finding is a split, not a table. Every phenomenon below is a dynamic — a shape a system's behavior takes over time, describable without any human present (a gap that never closes, a state that spreads, a value that overshoots and self-corrects). Separately, each has a typical human experience attached — but that attachment turned out to be conditional, not fixed. The same spring physics produced "trust" in one build and "relief" in another, depending only on whether the displaced object was something the observer felt was theirs to lose. The same reward-timing math produced "hope" in one context and flat "compulsion" in another. So the table below is a table of dynamics. The experience column is a hypothesis, annotated with the conditions it depends on. Get the conditions wrong and the same element can misfire or go silent — this happened to us repeatedly, and every rebuild in this project's history was, in retrospect, a correction to a coupling condition, not to the underlying dynamic.
Coupling conditions — referenced throughout
AgencyDoes the observer control the system's actor, or only watch it?
StakesIs anything shown identified as "yours" — a body, a possession — that can be lost?
TempoIs the rate of change slow enough to be felt as a process, not just seen as a jump?
ObservabilityIs the mechanism's operation itself visible, or only its outcome?
RepetitionDoes the observer experience this once, or many times? Some elements only resolve to their named feeling on repeat exposure.
ContrastIs a visible alternative/opposite case present in the same field? Some relational elements are illegible without one.
The table
Ten families. Numbered sequentially within family, not alphabetically. Click any element to expand it.
I
Pursuit
A persistent gap between a seeker and a target is the substance of the phenomenon — not the seeker, not the target, the gap itself.
1
Ac
Asymptotic Convergence
A seeker's approach rate decreases in proportion to remaining distance, so the gap shrinks forever without closing.
Underlying dynamicposition += (target − position) × k, k constant. Geometric decay of the gap; never reaches exactly zero.
Typical human experienceUnder self-directed framing (the target is "yours" to reach), longing. Under direct-agency framing (you are the seeker, controller in hand), the same math instead reads as mild frustration or determination — a different report from identical physics.
What must be trueApproach must be proportional, not fixed-step. The target must keep moving under its own logic (a stationary target degrades this into ordinary settling — see Homeostatic Return, Family III).
Differs from neighborsHomeostatic Return also approaches proportionally, but converges to a fixed rest point after a bounded excursion. This element's target never stops relocating, so the gap is sustained externally, not resolved internally.
Observed in: "longing," Interactive Feelings.
A pursuit relationship where the target is itself pursuing something else, so both parties are in simultaneous, coupled, unscripted motion.
Underlying dynamicChaser heading = vector toward nearest "leader"-type entity; leader's own heading is independently reactive (e.g. ballistic + bounce-on-contact), producing a pursuit curve toward a non-cooperative, non-stationary target.
Typical human experienceCompelling / absorbing rather than personally wistful — closer to watching a nature documentary than being addressed. Requires absent agency and no represented self in the scene; adding a controllable avatar into the same system was not tested but is predicted to collapse this back toward Asymptotic Convergence.
What must be trueAt least one population with reactive (not scripted) motion serving as the pursuit target. Density high enough that several simultaneous chases are visible at once.
Differs from neighborsAsymptotic Convergence's gap shrinks toward a limit on average; here nobody's gap reliably shrinks at all — targets keep escaping via their own physics. The phenomenon is the shape of many overlapping chases, not the felt failure of one.
Observed in: FollowLeaderType0 + Bounce + TypeDrift universe — rated 🤯 four independent times across the human-curated search, the strongest single signal in that entire study.
A system that appears to be approaching a completable state, until the completion condition itself triggers a rule that removes or defers completion.
Underlying dynamicOn (remaining-count ≤ 1): nonzero probability of spawning new instances of the goal, resetting the count upward before the terminal state is reached.
Typical human experienceCompulsion to continue, concentrated specifically at the threshold — not simple endlessness. An infinite supply that was never going to end does not produce this pull on its own; it is the near-completion, specifically, that hooks.
What must be trueA visible, countable "remaining" quantity. A non-zero but non-certain completion chance — true impossibility reads as rigged/broken rather than compelling, confirmed directly across this project's own iteration history.
Differs from neighborsErratic Target-Lock has no defined "done" state at all. This element specifically dangles one, then mostly withdraws it.
Observed in: "obsession," final build, Interactive Feelings — two earlier builds (score/streak framing; residue/futility framing) both failed to produce this before the near-miss + denial mechanic was isolated.
II
Propagation
How an effect spreads through a population from a point of origin — the family is ordered by how far the trigger's authorship can be traced.
State change occurs only at the moment of direct collision between two entities, and does not spread further on its own.
Underlying dynamicon(collision(a,b)): apply(effect, b) — single-hop, no re-triggering.
Typical human experienceReads as mechanical and legible — cause and effect tightly paired, producing a felt sense of control. Functions as the baseline against which the rest of this family reads as increasingly uncanny.
What must be trueA collision rule and a state-change rule with no recursive re-application to the newly-changed entity.
Differs from neighborsUnbounded Cascade is the identical rule with recursion switched on — this is that switch's "off" position.
Observed in: baseline Chain Slide activation rule.
A state change at one entity is sufficient by itself to trigger the identical rule at whatever it touches next, with no depth limit.
Underlying dynamicSame collision rule as Contact Transfer, made re-entrant: newly-activated entities immediately become triggers themselves within the same input.
Typical human experienceOne small input producing disproportionate downstream effect. Reads as satisfying while the chain stays attributable to that one input; reads as alarming once it outruns the ability to track it causally.
What must be trueRe-entrant triggering, plus population density sufficient that a further collision is likely per activation — below that density, cascades fizzle after one step and this collapses back toward Contact Transfer.
Differs from neighborsField Contagion needs no literal contact chain at all; this element still requires an unbroken sequence of discrete collisions.
Observed in: Chain Slide "Auto-Cascade" variant.
State change propagates to anything within a radius of an already-changed entity, regardless of who moved or who is causally "responsible."
Underlying dynamicEach tick, scan entity pairs within radius r; if one is in state X and the other is not, flip the other — ownerless, environmental, symmetric.
Typical human experienceLoss of causal tracking — "I don't know why that lit up." The element most often described with words implying weather or infection rather than an actor.
What must be trueProximity-based, not contact-based, trigger; no requirement that either party moved this tick.
Differs from neighborsUnbounded Cascade requires an unbroken sequence of discrete collisions; this element can activate two entities that never moved, via a third drifting near both.
Observed in: Chain Slide "Proximity Trigger" variant.
III
Equilibrium
Systems with a characteristic response to displacement from a rest state — this family is organized by whether the restoring force is present, absent, or intermittently overridden.
9
Bb
Non-Periodic Boom-Bust
A system displaced from a rest position experiences a restoring force proportional to displacement, and reliably settles back at that point after a bounded excursion.
Underlying dynamicDamped spring: force = −k·displacement − friction·velocity. Guarantees convergence to a single fixed point within the system's operating range.
Typical human experienceTrust and relief are both reported from this exact dynamic, distinguished entirely by coupling conditions: if the displaced entity reads as "you" or something held/dropped, the settle reads as trust; if the displaced quantity is your own internal tension, it reads as relief. Same spring, different self-reference.
What must be trueNegative feedback proportional to displacement, and — critically — a visible excursion past the rest point before correction. A spring that never overshoots reads as merely smooth, not reassuring; the overshoot is what recruits the fear the return then resolves.
Differs from neighborsAsymptotic Convergence (Family I) has a moving target it never reaches; this element has one fixed point it always reaches. Near-opposite shapes.
Observed in: "trust" (the dip-then-catch), "relief" (the tension spiral), Interactive Feelings.
A demand or difficulty variable grows at a rate that permanently outpaces the observer's fixed response capacity.
Underlying dynamicSpawn interval decreases monotonically with elapsed time, uncoupled from player performance; human reaction time is roughly constant, so the deficit compounds without bound.
Typical human experienceEscalating urgency terminating in overwhelm, not mastery — distinct from conventional difficulty curves, which are typically tuned to stay barely-beatable. This element is specifically what appears when that ceiling is removed.
What must be trueA growth-rate parameter with no negative feedback from success, plus an ambient aggregate signal (shake, vignette) so the trend, not just each individual failure, is legible.
Differs from neighborsHomeostatic Return has a rest point; this element is that family specifically for the case where the restoring force is deliberately withheld.
Observed in: "panic," Interactive Feelings.
A population converges toward homogeneity, then is fractured back toward heterogeneity by an unrelated renewal process, repeatedly, without ever settling into a fixed period.
Underlying dynamicA convergent rule (dominance-based conversion) pulls toward monoculture; an uncoupled renewal rule (age-triggered death-and-respawn) reintroduces diversity at intervals that are themselves irregular, since they depend on the age distribution the "boom" phase accumulated.
Typical human experienceReported as narratively legible — "rise and fall" — despite arising from two non-narrative rules sharing no clock. Possibly the clearest case in this study of pure structure producing a story-shaped read with zero authored content.
What must be trueOne convergent rule and one renewal rule on different, uncoupled timescales. If they share a clock, the result collapses into simple periodic oscillation, which reads as mechanical, not narrative.
Differs from neighborsRunaway Escalation is one-directional and single-variable; this element requires at least two counteracting rules and produces genuine reversals.
Observed in: Universe #60 (FollowLeaderType0 + DominantConvert + AgingDecay), headless search and human-curated gallery.
IV
Scarcity
Conservation laws governing how much of a state can exist, and what happens when it is contested.
An active/marked state can be held by only one entity at a time; granting it to a new holder revokes it from the previous holder.
Underlying dynamicon transfer(a→b): state(a) = off; state(b) = on. Strict conservation — total "on" count invariant.
Typical human experienceA sense of stewardship or responsibility ("I have to keep it moving"), rather than accumulation — meaningfully different from a rule that merely copies state (Contact Transfer), where nothing is ever at risk of being lost.
What must be trueThe transfer rule must explicitly clear the source's state on hand-off, not merely set the destination's.
Differs from neighborsZero-Sum Diversion moves accumulated quantity between two persistent pools; this element moves a single token of state between individual entities in one population.
Observed in: Chain Slide "Charge Transfer" variant.
An action nominally directed at increasing one pool is, some fraction of the time, invisibly redirected to increase a rival pool instead.
Underlying dynamicon(action): with probability p, credit pool B instead of pool A — typically paired with a visible transit animation, so the diversion is perceptually legible as theft rather than noise.
Typical human experienceEnvy, specifically — distinguished from ordinary unfavorable comparison (watching a faster independent process) by the visible transit. Removing the transit and leaving two independently-growing pools demoted the identical probability structure to flatter "falling behind," confirmed directly in this project's own before/after.
What must be trueTwo comparably-styled accumulators; a diversion probability low enough to stay intermittent (p=1 reads as broken/absurd, not unfair — most actions must succeed normally for the exceptions to register as theft).
Differs from neighborsRunaway Escalation is an ungoverned rate; this element is a governed, comparative, zero-sum rate where two parties' fortunes are causally coupled.
Observed in: "envy," final build, Interactive Feelings.
V
Memory
How a system encodes and carries its own history forward — ordered by what, exactly, is remembered: a place, a moment, or a rule.
An event at a location permanently alters the future behavior of that location itself, independent of which entities later occupy it.
Underlying dynamicon(event at cell c): scars.add(c); thereafter any entity at c triggers the effect unconditionally, forever, regardless of its own type or history.
Typical human experienceAn uncanny sense that the world, not the pieces, is what's accumulating — reported as distinct from ordinary progress-saving, closer to haunting, once enough scars accumulate that the field's behavior stops being predictable from its current visible state.
What must be trueThe effect must attach to spatial coordinates, not entity identity. Resets that clear entity state must not clear the scar record, or this collapses into ordinary non-memorable play.
Differs from neighborsRule Accretion changes what is true everywhere (the rules); this element changes what is true about specific places (the state).
Observed in: "Rule Residue" study — the reset-vs-scar behavior was found by direct testing, not predicted in advance.
Information revealed by an action fades back toward its hidden state over time, so legibility depends on continued attention, not cumulative effort.
Underlying dynamicon(reveal): opacity(region) −= k; every tick, unconditionally: opacity(region) += small constant. A leaky reveal — a bucket with a hole.
Typical human experienceA mild, recurring "wait, what was that again" — notably does not accumulate into the frustration of Runaway Escalation, because the decay rate is tuned far slower than the reveal rate, so net progress stays possible. The phenomenon is friction, not a hard block.
What must be trueReveal rate must exceed passive decay rate (otherwise nothing is ever knowable — plain concealment, not this). Decay must be unconditional and global, not triggered specifically by the user's absence.
Differs from neighborsPermanent Scarring is one-way and unbounded; this element is explicitly bounded by its own leak.
Observed in: "curiosity," Interactive Feelings.
The consequence of an event is not a change in world-state but a permanent change in the rule that governs future events of that same kind.
Underlying dynamicon(event of type T at location L): globalRules[L] := new_rule; all future evaluation at L uses the newly-installed rule.
Typical human experienceWhen noticed at all, the most conceptually destabilizing element in the table — a sense that "this is a different game than the one I started." Most subjects needed the effect pointed out before noticing it, which may itself be a property worth its own entry (provisionally: low observability).
What must be trueThe rule-table itself must be mutable at runtime and addressed by the same coordinates as the state it governs, and must persist across resets that would otherwise clear state.
Differs from neighborsThe sharpest edge case in the table: in our own implementation, Permanent Scarring and Rule Accretion were nearly indistinguishable by construction (a scar's only effect was a rule change at that cell). Flagged unresolved — see closing notes.
Observed in: "Rule Residue" study, as the study's own framing — not yet cleanly isolated from Permanent Scarring in an implementation.
VI
Revelation
The relationship between what is knowable and what is currently shown.
The observer can reveal fragments of a fixed, complete underlying structure through local interaction, but no single moment ever shows the whole.
Underlying dynamicA static ground-truth layer beneath a dynamic occlusion layer, cleared locally around the point of interaction (and typically re-applied over time — see Decaying Trace).
Typical human experienceCuriosity, specifically when the fragments imply — via partial symmetry or recognizable partial shapes — that a coherent whole exists to be found. The same mechanic over patternless ground truth tends to flatten into idle fidgeting, since there is no coherent completion to anticipate.
What must be trueGround truth with structure above the noise floor; an occlusion mechanism responsive enough to feel controllable.
Differs from neighborsThis element implies a knowable, finite answer merely hidden. Bounded Ambiguity implies there may be no edge to find at all.
Observed in: "curiosity," Interactive Feelings.
A single, discrete event recontextualizes an object previously understood as the entire system into a small part of a much larger one.
Underlying dynamicA reference-frame transform whose parameter jumps or eases between two fixed extremes, changing what one spatial unit is perceived to represent, without altering the object itself.
Typical human experienceAwe, specifically the "vastness exceeding one's current mental model" variant — but only if the reframing is a genuine surprise. A reframing the observer sees coming reads as merely zooming out, much flatter.
What must be trueThe pre-reframe state must be genuinely legible as complete-in-itself. The trigger must be tied to the observer's continued attention (visibility), not a fixed clock the observer can preempt by looking away.
Differs from neighborsThis element is a discrete, one-time event resetting the unit of comprehension. Bounded Ambiguity is a continuous, standing property that never resolves into a discrete moment at all.
Observed in: "awe," Interactive Feelings — required two separate bug fixes (a mistimed trigger, then a mistargeted trigger) before the intended experience actually emerged. See closing notes on observability.
The edge of a visible field is deliberately unresolved — faded, not terminated — so the observer cannot determine whether the field is finite or merely un-rendered beyond that point.
Underlying dynamicA rendering falloff (opacity or density gradient) applied at the boundary of an otherwise-enumerable, finite structure, deliberately concealing that it is enumerable.
Typical human experienceA component of awe distinct from Scale Reframing: where Reframing supplies the surprise, this element supplies the durability of the feeling afterward. A hard-edged, countable version of an otherwise-identical field was independently reported as "meh."
What must be trueThe underlying structure must actually be finite (this is a rendering choice, not a claim about the data); depth or density variation in what is rendered, so the fade reads as continuing into haze rather than abruptly stopping.
Differs from neighborsDecaying Trace's gradient is temporal (time since interaction); this element's gradient is spatial and static (distance from center).
Observed in: "awe," second build, Interactive Feelings.
VII
Relation
How multiple independent agents' behaviors couple, or fail to couple, with each other.
18
Ms
Mutual Synchronization
19
Nr
Active Non-Reciprocity
Independent entities, each following only local rules with no shared controller, converge toward shared position, state, or phase.
Underlying dynamicEach entity's next-state is a function of its neighbors' current states (attraction, alignment, or averaging), with no global broadcast — coherence is emergent, not instructed.
Typical human experienceThe entities are read as "belonging to each other" — but this requires the observer to also see entities that are not synchronized in the same field, as a contrast group. A fully-synchronized population with nothing outside it tends to read as merely a pattern, not a relationship.
What must be trueLocal, not global, coupling rule; a population large enough (≥3) that "belonging" reads as a group property.
Differs from neighborsErratic Target-Lock (Family I) is asymmetric — one role chases, another flees or wanders. This element is symmetric: every entity plays the same role toward every other.
Observed in: "loneliness" (the bonded background figures); Universe Gallery flocking-family movement laws (SeekUnlike, Orbit).
One party's proximity or effort toward another produces no positive response, and specifically produces active avoidance rather than mere non-response.
Underlying dynamicEntity velocity includes a repulsion term keyed specifically to one designated "outsider," while the same entities carry an attraction term toward each other — Synchronization toward the in-group and Non-Reciprocity toward the outsider, simultaneously, in one population.
Typical human experienceLoneliness — distinguished, across two builds of this project, from mere passive indifference, which was reported as reading like "a screensaver." The active, directional avoidance term was the specific, load-bearing change between the versions.
What must be trueRequires Mutual Synchronization present in the same scene as contrast. The outsider must be visually a peer-category entity (same rendering language), or the avoidance reads as physics rather than rejection.
Differs from neighborsZero-Sum Diversion (Family IV) is about contested resource, legible via a visible transit of "stuff." This element is about contested relation, legible via avoidance, with nothing material changing hands.
Observed in: "loneliness," second build, Interactive Feelings.
A population sorts itself into same-type clusters, or spreads into a maximally-dispersed arrangement, purely from a local same/different-type rule.
Underlying dynamicMovement bias toward (clustering) or away from (dispersion) the nearest same-type neighbor, iterated until a stable or slowly-evolving macro-pattern emerges.
Typical human experienceNotably topic-dependent: clustering reads as neutral-to-positive; forced dispersion (an objective requiring no two active pieces share a line) was reported as puzzle-like cognitive tension rather than any named feeling — suggesting this element may sit closer to Family I's cognitive character than to Relation's social character. Flagged for possible re-classification.
What must be trueA symmetric same/different comparison rule; density sufficient that clusters or dispersed lattices read as pattern, not noise.
Differs from neighborsSynchronization needs only an attraction term and produces one shape. This element needs a same/different discrimination and can produce two opposite macro-shapes from the sign of the same rule.
Observed in: Chain Slide "Fracture" objective; Universe Gallery FleeLike-family movement laws.
VIII
Divergent Resolution
Systems deliberately engineered so the apparent trajectory of an action and its actual outcome diverge.
21
Sj
Signaled Jeopardy, Guaranteed Safety
22
Sd
Signaled Success, Denied Outcome
An action is staged to visually imply risk of failure, while the underlying rule guarantees success every time — the guarantee is only learned through repetition.
Underlying dynamicAn apparent free-fall or overshoot that a spring rule always, without exception, arrests before a failure threshold — the risk lives entirely in the motion, not the state machine.
Typical human experienceTrust, specifically as a property that must be built, not stated. First exposure reads as suspense; only after several repetitions — once "it always comes back" is personally confirmed, not merely told — does the report shift to trust. This suggests trust may not be a single-exposure phenomenon at all.
What must be trueA deterministic (not merely high-probability) safety guarantee, and a genuinely alarming-looking excursion — a barely-perceptible dip doesn't recruit enough initial fear for the later relief to register.
Differs from neighborsHomeostatic Return (Family III) is the same spring mechanic; this element specifically names the coupling condition — an object read as "held" or "dropped," at stake — required for that mechanic to be reported as trust rather than mere relief.
Observed in: "trust," second build, Interactive Feelings.
An action is staged to visually imply near-success — a wobble, a flinch — while the underlying rule frequently or always withholds the completion that was implied.
Underlying dynamicA near-miss detection radius wider than the true hit radius, triggering a distinct "so close" animation on miss, paired at the population level with completion-denial (Denied Terminus, Family I).
Typical human experienceThe compulsive-retry component of obsession — distinguished from Denied Terminus by operating on the felt closeness of one action, not the population's completion count. The two were combined in the working build; it's not yet established whether either alone is sufficient.
What must be trueA near-miss radius detectably wider than the hit radius, with visible motion feedback specifically on the miss — a silent near-miss did not appear to register.
Differs from neighborsNear-exact structural mirror of Signaled Jeopardy / Guaranteed Safety (apparent-good/actual-neutral vs. apparent-bad/actual-good) — included in the same family to test whether divergence direction is meaningful. Provisionally: yes. The mirrored pair produced compulsion and trust respectively, not the same feeling twice.
Observed in: "obsession," final build, Interactive Feelings.
An action's outcome is computed but deliberately withheld for a fixed interval, decoupling the moment of the act from the moment of knowing its consequence.
Underlying dynamicon(action): schedule(resolve, delay=k); no state change is visible until the scheduled resolution fires, regardless of further input during the interval.
Typical human experienceA "held breath" quality distinct from ordinary latency — the felt difference from simple slow response appears to be that the delay is constant and gets anticipated, at which point the interval itself, not the eventual result, becomes the site of the feeling.
What must be trueDelay long enough to be consciously noticed (tens of milliseconds reads as lag; several hundred appears to be the threshold observed here) and short enough not to read as the system having stalled.
Differs from neighborsNon-Periodic Boom-Bust (Family III) is a visible, ongoing oscillation the observer watches happen in real time. This element hides the outcome entirely during its own interval, trading visibility for anticipation.
Observed in: "hope," second build, Interactive Feelings.
IX
Rhythm
Asymmetries and structures in the timing of a system's own responses, independent of what state is actually changing.
24
Br
Build/Release Asymmetry
25
Vr
Variable-Ratio Reward
The rate at which a quantity accumulates under sustained input differs from the rate at which it dissipates once input stops, in a specific direction.
Underlying dynamicd(quantity)/dt = +k1 while input held, −k2 while released, with k2 > k1.
Typical human experienceRelief, specifically tied to the direction of asymmetry — slow build, fast release. The untested reverse (fast build, slow release) is predicted by the same logic to read closer to dread or resignation. Open test.
What must be trueTwo distinct, direction-dependent rate constants, and a visible representation of the accumulating quantity — the asymmetry has no felt effect if the quantity itself is invisible.
Differs from neighborsThis element is deterministic and continuous; Variable-Ratio Reward is probabilistic and discrete (single trigger events, not a held quantity).
Observed in: "relief," Interactive Feelings.
A repeatable, low-cost action produces a reward whose timing and magnitude are unpredictable, with a small chance of a substantially larger-than-average payout.
Underlying dynamicon(action): sample a weighted distribution skewed toward small/no reward with a long right tail.
Typical human experienceThe one element here with an established name outside this study (the slot-machine mechanism) — included specifically because it underwrote both "hope" and obsession's near-miss loop, suggesting the same distribution supports two differently-valenced experiences depending on whether the framing implies fighting for an outcome against real odds, versus simply farming it.
What must be trueA skewed, not uniform, reward distribution; action cost low enough to repeat many times per minute.
Differs from neighborsThis element's randomness is in the magnitude of a frequent success. Signaled Success / Denied Outcome's randomness is in whether a clearly-aimed-for completion happens at all.
Observed in: "hope" and "obsession," Interactive Feelings — same underlying element, divergent experience. See closing notes.
An action that would otherwise succeed by ordinary contact rules is instead rejected unless it occurs at the correct position in a required sequence.
Underlying dynamicA pointer into a fixed ordered list of required events; on(candidate): succeed only if candidate equals the pointer's current target, else reject with no state change; on success, advance the pointer.
Typical human experienceThe tension of a known shortcut being deliberately denied — requires the shortcut to be genuinely reachable and rejected specifically for being out of order, not for being unreachable. An order enforced purely by level geometry (you cannot physically reach step 3 first) did not produce this same felt tension, since there is nothing to notice being denied.
What must be trueA sequence pointer, plus at least one genuinely reachable path that violates the required order, for the gate to have anything to actually reject.
Differs from neighborsDenied Terminus (Family I) denies completion probabilistically and repeatedly at the same threshold. This element denies specific out-of-order attempts deterministically, and permits completion unconditionally once order is correct — persistence versus correctness.
Observed in: Chain Slide "Relay" objective.
X
Perpetuation
— set apart, see note
Not a family of experiences like the other nine — a property that modulates the others, the way a catalyst is discussed separately from the reactants it acts on. Included because removing it, holding everything else constant, reliably collapsed several named phenomena above back into flat monoculture.
27
Sn
Sustained Non-Convergence
A system's aggregate state keeps changing in structurally novel ways indefinitely — settling into neither a fixed point, a short repeating cycle, nor statistical noise indistinguishable from randomness.
Underlying dynamicNot a single mechanism but a diagnosis: absence of three failure modes (flatlined activity; state-hash cycling at short period; a clustering metric staying within the noise band of a randomized control) sustained across a long observation window.
Typical human experienceThe property that made 40 of 100 headless universes worth watching at all — though roughly a third of those turned out, on closer inspection, to be a fourth failure mode the original test missed entirely (full convergence to a frozen monoculture that merely kept moving cosmetically). The diagnostic itself should be treated as incomplete.
What must be trueEmpirically, at least one convergent rule and at least one renewal rule on different timescales (see Renewal Injection). Convergence alone reliably collapsed to stasis; renewal alone reliably stayed statistically indistinguishable from noise.
Differs from neighborsNon-Periodic Boom-Bust (Family III) is one specific, narratively-legible instance of this element; most instances of Sustained Non-Convergence do not organize into anything as legible as rise-and-fall.
Observed in: 100-universe headless search; Universe Gallery survivor classification.
A rule that reintroduces variance into a system independent of, and uncorrelated with, whatever convergent process is currently dominating it.
Underlying dynamicAt a rate uncoupled from the convergent rule's own dynamics (fixed-probability mutation per tick, or age-triggered replacement), overwrite some fraction of the population's state with fresh, unconverged values.
Typical human experienceNot independently felt — its entire signature is indirect, showing up only as the presence or absence of Sustained Non-Convergence and its instance, Boom-Bust. Removing it, holding everything else constant, reliably collapsed several otherwise-distinct favorites into flat monoculture — a strong "necessary but not sufficient" candidate, unique in this table.
What must be trueInjection rate slow relative to the convergent rule (faster and the system never organizes — pure noise) but fast relative to that rule's own timescale to full convergence (slower and renewal arrives too late to matter).
Differs from neighborsDecaying Trace (Family V) decays one specific prior action's visibility. This element introduces variance uncorrelated with any specific prior action, into the system as a whole.
Observed in: TypeDrift / AgingDecay / PopulationPulse field-rules, 100-universe headless search.