Apache License 2.0—see LICENSE for details.
Copyright (c) 2025 Woo Ker Yang (Patrick Woo) patrickwoo.1976@gmail.com
If you reference or adapt this framework, please credit Patrick Woo and this repository.
This documentation is still in development.
While every update aims for accuracy, some parts may still be incomplete or contain inaccuracies. I appreciate your understanding in this matter, and we apologize for any inconvenience this may cause.
This document serves as a detailed compendium of potential applications for the Frame-Persistent Stateless Randomisation (FPS-R) framework. While the main README.md establishes the core philosophy, this document explores the practical implementation of that philosophy across a diverse range of technical, creative, and strategic domains. While these domains attempt to show the broad area that FPS-R can be applied to, they are not exhaustive. I believe there will be a huge number of use cases will be discovered once the users understand the potential in the framework.
FPS-R as a composer of lifelike timing and motion.
This theme explores FPS-R as a grammar of expressive modulation—used to animate behaviour that feels real, alive, and intentionally imprecise. Whether powering an avatar’s hesitant eye shift, a prosthetic’s subtle posture correction, or a synthesiser’s phrasing drift, FPS-R injects rhythm and irregularity with poise.
Here, randomness is not noise—it’s performance. Modulation becomes motion. Hesitation becomes presence.
FPS-R contributes phrasing logic that is deterministic yet organic—producing expressive behaviour across AR, robotics, wearables, and musical systems without scripting or simulation overhead.
FPS-R augments synthetic perception systems with organic, non-repeating behavioural texture—introducing subtle timing variation, micro-drift, and decision hesitation across gaze, gesture, and stimulus response. In human-centered environments, where uncanny precision breaks realism, FPS-R fills the behavioural gaps between macro-intent and execution nuance.
Use Cases:
FPS-R Strengths Leveraged:
As robotics moves from automation to articulation—from machines that complete tasks to agents that participate—FPS-R offers a stateless modulation layer that injects micro-expressivity and intentional ambiguity into motion. Whether idle, transitioning, or deliberating, robots augmented with FPS-R move as if they mean it.
Use Cases:
FPS-R Strengths Leveraged:
🤖 FPS-R doesn’t just make robots move—it helps them hesitate, drift, reconsider, and breathe.
In assistive systems—prosthetics, exosuits, haptic wearables—functionality is essential, but expressivity is transformative. FPS-R doesn’t control the limb; it choreographs its timing. It introduces micro-variation, hesitation, and drift—not to mimic dysfunction, but to restore the organic texture of human motion.
This expressive modulation brings a sense of natural familiarity to robotic extensions—replacing the awkward rigidity common in many current devices with motion that feels quietly alive. For users, this fosters psychological acceptance and embodiment. For interaction partners, it enables social ease and comfort. And for the wearer, it offers not just utility, but dignity—a restoration of presence, fluidity, and human rhythm.
Use Cases:
FPS-R Strengths Leveraged:
🫀 FPS-R doesn’t make assistive systems smarter—it makes them feel more human.
Biofeedback systems sense and interpret the body’s internal state—but it’s their response that makes them felt. FPS-R serves as a temporal expression layer, translating biometric signals into nuanced, non-repeating feedback that guides, soothes, and signals without overwhelming.
Where assistive robotics actuate on behalf of the user, biofeedback systems speak to the user—and FPS-R ensures that voice is rhythmic, responsive, and human-feeling.
Use Cases:
FPS-R Strengths Leveraged:
🎵 FPS-R gives biofeedback systems a voice—not loud, but resonant.
Swarms and autonomous coverage systems often fall into deterministic loops—predictable, mechanical, and easily exploitable. FPS-R injects organic timing variation and stateless differentiation, enabling fleets to behave with emergent realism and expressive unpredictability.
🧰 Use Cases:
🔧 FPS-R Strengths Leveraged
Ambient and embedded systems often operate with tight constraints—limited memory, low power, real-time requirements. FPS-R introduces expressive modulation into these systems without breaking the bank on logic complexity or storage. 🧰 Use Cases:
🔧 FPS-R Strengths Leveraged:
FPS-R syncs not just to linear time, but to musical structures—bars, beats, swings, syncopation. This rhythmic awareness transforms FPS-R into a musical decision engine, where modulation is phrased rather than triggered.
🧭 Overview By locking into tempo grids and rhythmic thresholds, FPS-R enables non-repeating musical behaviour that feels intentionally structured. It supports everything from generative loops to expressive controller behaviour, producing motion that grooves, glitches, and phrases like a musician.
🛠 Categories and Use Cases 🎵 Generative Composition & Rhythmic Systems
🎵 Note: By syncing modular and switching logic to musical timing grids, FPS-R becomes not just a procedural tool—but a tempo-sensitive composer, capable of phrasing with nuance and glitching with groove.
🎹 Expressive Instrument Modulation
🎛️ Ideal for generative soundscapes, modular patches, and live adaptive scoring.
📻 Sonic Emulation and Circuit Temperament
🔄 FPS-R doesn’t mimic electronics. It channels their mood.
👂 Sound Design and Affective Rhythm
🔧 FPS-R Strengths Leveraged
🎼 FPS-R doesn’t just keep time—it listens to it.
FPS-R as a deterministic stress engine for critical systems.
In this theme, FPS-R is deployed not for beauty, but for pressure—for surfacing edge cases, testing robustness, and generating repeatable entropy in fragile systems. Whether simulating packet jitter, cybersecurity breach patterns, financial flash crashes, or protocol escalations, FPS-R functions as a truth machine—replaying chaos with mathematical control.
It’s not about what a system should do under load. It’s about what it phrases when pressured—and what that says about its assumptions.
FPS-R contributes controlled unpredictability, stateless variation, and deterministic replay to domains like software testing, adversarial simulation, and infrastructure resilience.
In cybersecurity, attackers often use automated tools to probe systems, and defenders use analytical tools to detect these patterns. The success of both depends on figuring out the “what” (the type of attack or defense) and the “when” (its timing). While many systems focus on the “what,” the “when” is a critical and often overlooked layer of strategy.
FPS-R acts as a deterministic chaos engine for both attackers and defenders, with a unique strength in obfuscating the “when.” It generates realistic, layered threat behaviour with replayable entropy—ideal for red/team blue team parity, post-mortem forensics, and training under chaos.
The Power of Obfuscating the “When” By introducing a phrased, unpredictable rhythm to defensive or offensive actions, you can gain a significant advantage. An attack or defense that uses a “move-and-hold” rhythm is much harder for automated tools to distinguish from legitimate, human-driven traffic. This “phrasing” can effectively hide your actions in the noise, creating a “moving target defense.” An attacker may know what vulnerability to target, but if the window of opportunity is unpredictable, it makes it much harder to execute a successful attack.
Use Cases:
FPS-R Strengths Leveraged:
This section outlines a novel multi-factor authentication protocol that leverages FPS-R to enhance security. It serves as a more secure, dynamic alternative to the current standard of Time-Based One-Time Passwords (TOTP), which rely on a fixed, predictable 30-second refresh interval.
The “Secret Handshake” Protocol This new protocol introduces a “secret handshake” that establishes an unpredictable, phrased rhythm for when new authentication codes become valid, making timing-based attacks significantly more difficult.
The Protocol in Context This protocol is designed as a Multi-Factor Authentication (MFA) system. It provides a secure second factor that a user or machine provides after a primary authentication method (like a password) has been successful. The core innovation is replacing the fixed time interval of TOTP with a secret, deterministically generated, and unpredictable one.
Phase 1: The One-Time Setup This foundational step happens only once when a user enrolls a new device.
At the end of this step, both the server and the client securely store the exact same master secret key.
Phase 2: Login and Re-synchronization (The “Secret Handshake”)
The synchronisation tuple would look like this:
// Define a struct for the synchronization packet
typedef struct {
int start_time;
int fpsr_index;
int cycle_time_min;
int cycle_time_max;
int number_of_cycles;
int playbook_idx;
int algorithm_idx;
int fpsr_params_idx;
} FpsrSyncPacket;
start_time: A Unix timestamp (seconds since epoch) to anchor the sequence in real-world time and help detect clock drift.fpsr_algorithm_index: The integer number to indicate the FPS-R algorithm used, ensuring both sides use the same engine.cycle_time_min & cycle_time_max: An array that maps FPS-R’s normalized 0-1 output to a specific range of real-world hold durations (e.g., a randVal of 0.5 might map to a 42-second refresh interval).number_of_cycles: An integer defining how many refresh cycles both sides will independently generate before they must perform a new handshake.playbook_idx: Selects a specific LUT playbook (e.g., [0,0,1,2], [1,0,0,2,0,0,0,2,0,1,0,0], etc). Where:
0 - drop frame1 - Generate Auth Code2 - Generate Cycle Durationalgorithm_idx & fpsr_params_idx: A single integer that points to a specific, pre-shared set of FPS-R parameters (e.g., algorithm type, seeds). This avoids transmitting verbose settings, adding another layer of security.A crucial failsafe is built into the protocol: if any generated hold duration would exceed a maximum secure lifetime (e.g., 90 seconds), both client and server are programmed to reduce the hold duration by first attempting to reduce the number_of_cycles, failing which, both will discard the current frame and advance to the next valid frame in the FPS-R sequence. These deterministic logic are applied on both client and server ensure they are secure and will always remain in sync.
Mechanics of the Exchange
Upon a successful login periodic refresh, the server and client perform the secret handshake, securely exchanging the synchronisation tuple. From that point on, both systems operate independently, using the playbook_idx, fpsr_algorithm_index and fpsr_params_idx to select from a shared secret list of “playbooks” (e.g., [0,0,1,2]), FPS-R algorithms and related parameters.
Starting from the agreed-upon fpsr_index, both systems step through the playbook in a repeating loop to execute the required number_of_cycles. The length of the playbook and the number of required cycles are decoupled:
number_of_cycles is met.number_of_cycles is met, discarding the remaining tasks in the playbook.When the number_of_cycles cycles has been reached, the client and server goes for another round of secret handshake.
The is system ensures that the server and client can perfectly mirror each other’s timing and values. This creates a complex, phrased synchronisation rhythm that is unknown to outside observers and cannot be replicated.
Application in Machine-to-Machine (M2M) Authentication While the protocol is ideal for user logins, it is also a powerful tool for securing automated, machine-to-machine communication (e.g., between microservices or IoT devices). Standard, instantaneous M2M authentication can be predictable and vulnerable to interception or replay attacks.
This protocol introduces a “moving target defense.” By forcing machines to communicate according to a secret, unpredictable rhythm, it makes it incredibly difficult for an attacker to know the correct moment to intercept a valid credential or inject malicious data. The “convoluted dance” is not a bug; it’s a feature that hardens the communication channel against sophisticated, timing-based attacks.
In environments sensitive to market volatility and sequence-dependent decision logic, FPS-R produces reproducible shockwaves—ideal for system resilience testing, trading algorithm evaluation, and policy stress simulations.
Use Cases:
FPS-R Strengths Leveraged:
FPS-R excels at semantic stress-testing—generating inputs and sequences that feel chaotic but are rigorously defined and deterministic. It is ideal for surfacing edge cases, malformed input handling, and system assumptions under pressure.
Use Cases:
FPS-R Strengths Leveraged:
FPS-R can be used to simulate layered protocol behaviour, infrastructure churn, and network stress conditions across the OSI model—from physical transmission to application-layer anomalies. Its deterministic modulation enables reproducible chaos across distributed systems, ideal for testing resilience, timing, and fault tolerance.
Use Cases:
FPS-R Strengths Leveraged:
🧠 FPS-R doesn’t just simulate packets—it choreographs protocol behaviour across time.
FPS-R as phrasing logic for emergent futures and cognitive drift.
This paradigm treats FPS-R as a tool for modeling not what is, but what could unfold. It supports systems that explore escalation, imagination, and behavioural inference—shaping timelines that feel plausible, not predictable.
Here, phrasing becomes foresight—tempo as thought, rhythm as revelation.
FPS-R allows scenario architects to simulate not just what decisions are made, but when and how those shifts unfold. In systems involving governance, public sentiment, or adversarial coalitions, FPS-R introduces rhythmic plausibility into strategy modeling.
Use Cases:
FPS-R Strengths Leveraged:
While not adversarial in nature, these domains thrive on scenario generation, timeline variation, and failure recovery modeling—all of which align with FPS-R’s modulation logic.
Potential Contributions:
FPS-R Strengths Leveraged:
🧠 Cognitive Modeling and Generative Thought At its most abstract and powerful, FPS-R serves not merely as a modulation layer—but as a catalyst for cognition itself. In this speculative but increasingly tangible domain, it animates the inner workings of large language models—not by influencing their semantics, but by shaping their tempo of thought.
Thought as Temporal behaviour In systems like LLMs, FPS-R can function as a temporal pacing engine, modulating how attention flows—not uniformly, but with deliberate pause, drift, jump. A model can appear to deliberate when it holds. It can pivot when it jumps across semantic space. It can explore when it drifts along an unexpected arc.
This rhythm doesn’t alter content. It alters how content emerges—allowing cognition to express itself not only in what is said, but in how the system moves through thought space.
Structured Ambiguity: Fuzzy Logic Without Memory Within fuzzy logic systems, FPS-R can adaptively reshape thresholds—reflecting hesitation, confidence, uncertainty—not through retraining or historical state, but through procedural modulation.
Rules become porous. Boundaries breathe. Tokens delay or accelerate not by conditionals, but by timing.
Dialogue as Modulated Emergence In generative agents, FPS-R imbues conversation with lived rhythm. It becomes the expressive regulator of turns and tangents. When an assistant lingers on a thought, pivots to a related metaphor, or re-engages a dropped thread five messages later—that is FPS-R as dialogue dramaturgy.
Topic coherence no longer requires memory. It emerges from timing logic alone.
Latent Drift as Procedural Cognition Most profound of all: FPS-R may define the shape of synthetic ideas as they traverse latent space. Between a start vector and an end vector—two concepts, prompts, or goals—FPS-R doesn’t simply interpolate. It generates a modulated trajectory, sculpted by jump-hold-drift behaviours, that samples meaning with compositional curvature.
Each waypoint along this arc reflects conceptual drift that is not random, but phrased. What appears as wandering attention is in fact procedural guidance through token space. In this way, FPS-R encodes semantic emergence as rhythm, and unlocks a form of path-dependent creativity—where how one moves through latent space becomes what is expressed.
This is how creative minds truly think.
A system modulated by FPS-R can exhibit behaviour we associate with cleverness, spontaneity, even brilliance. A drifting thought that stumbles into metaphor. A tangent that loops back with a joke. A moment of hesitation that results in exactly the right phrasing.
By embedding timing as meaning, FPS-R makes personality tunable. Some capsules create focus. Others simulate curiosity. And some—deliberately—introduce the kind of structured derailment that makes conversation sparkle.
This is how synthetic thought becomes creative: not by predicting the next word, but by moving through context with rhythm and intuition. It’s how an LLM stops sounding like a completion engine and starts sounding like someone you want to keep talking to and thinking with.
Not just a model of thought—but a choreography of cognition. Not a shortcut to intelligence—but the long way around, where the view is better. 🌀 Here, simulation becomes origination. behaviour becomes thought. And thought begins to phrase itself.
Once a behaviour can be captured and mapped into FPS-R space, it doesn’t just exist in isolation—it becomes an entry point into a modulatable reality.
You’re not just fitting motion—you’re anchoring intent in a system that can extrapolate.
This section offers a glimpse into how FPS-R can perform what is essentially reconstructed time travel through phrasing.
FPS-R is a deterministic and parameterised mathematical model with its own internal logic. Its analytical power lies in its ability to model, express, and procedurally generate observed behaviour using structured phrasing patterns.
When researchers identify a behavioural pattern—its rhythm, tempo, or gestural contour—they can attempt to fit it to an FPS-R function. This involves describing the observed pacing and value changes, then seeking a matching FPS-R curve that echoes its motion, inflection, and intervals between holds and jumps.
This matching process may include:
The more aspects of phrasing that align—rhythmic cadence, modulation shape, move/hold balance—the higher the model confidence. A short match may be coincidence. A long match suggests behavioural resonance. Once the best fit is found, FPS-R acts as a generative analog of the observed phenomenon.
This fit unlocks a profound capability: procedural extension in both temporal directions.
The result is a temporal grammar of phrasing. You’re no longer modeling behaviour alone—you’re capturing its trajectory of becoming.
This doesn’t apply only to motion. It can be extended to any system with observable inflections:
This is not a tool for prediction. It is a framework for structured possibility, constrained by phrasing parameters—not random invention.
FPS-R offers procedural insight into system readiness: How well is a process, actor, or interface prepared to handle state changes that could arise under this modulation envelope? By studying future and past timelines generated under a matching phrasing rule, we gain visibility into both what was plausible, and what might remain consistent going forward.
This use case is a speculative future possibility. It assumes an AI that has been trained to identify specific movements—more probably horizontal movement (perpendicular to the the camera’s axis to the object)—and is able to extract the movement profile in real time, and match an FPSR profile for in settings and frame number to the motion currently taking place. Imagine pointing a camera at a candle’s flicker or a leaf’s tremble. An AI matches an FPS-R configuration to its phrasing rhythm. Onscreen, the system now generates:
What appears is not simply replay—but a plausible procedural history and future, based on phrasing grammar.
That’s not just modeling.
That’s expressive reconstruction.
And because FPS-R generates phrasing deterministically from fixed seeds and settings, this reconstruction is fully reproducible, portable, and analyzable. Researchers, designers, or observers are free to study the unfolding, not just view it.
FPS-R transforms moments into modulation fields—spaces where behaviour becomes explainable, extensible, and legible through phrasing alone.
FPS-R as a Co-Orchestrator of Simulations
Insight: bugs emerge not from the combination itself, but from the timing of its propagation.
This is especially relevant in: Distributed systems, Multi-agent coordination, UI/UX feedback loops, Sensor fusion pipelines.
rand() hops values aggressively, FPS-R can:This allows us to test:
A new kind of simulation:
Not just “what happens when everything changes,” but “what happens when some things wait while others jump.”
This is where edge happenstance lives:
And yes, they’re hard to catch. But FPS-R gives you a grammar to provoke them—not through brute force, but through expressive pacing.
| Concept | Description |
|---|---|
| Temporal Drift Testing | Injecting expressive delays to test causal propagation and subsystem lag |
| Causality-Stagger | Simulation Modeling how decisions ripple unevenly across a system |
| Expressive Perturbation | Using FPS-R to modulate timing, not just values |
| Hold-then-Break Diagnostics | Observing system behaviour during expressive delay before state transition |
Digital twins traditionally aim for state mirroring—replicating the physical system’s data, structure, and behaviour in real time. But what’s often missing is expressive timing and causal nuance. That’s where FPS-R enters:
FPS-R transforms the digital twin, opening doors to:
| Twin Component | Traditional Approach | FPS-R Enrichment |
|---|---|---|
| State Transitions | Deterministic or noisy | Expressive, frame-persistent randomness |
| Timing Behavior | Rigid or synchronized | Hesitation, drift, staggered causality |
| Agent Coordination | Rule-based or optimized | Emergent offsets, behavioral diversity |
| Edge Case Discovery | Combinatorial fuzzing | Temporal perturbation and expressive lag |
FPS-R as a deterministic engine for exploring probabilistic worlds.
It is crucial to understand that FPS-R is not a scientific model of reality in itself. It contains no intrinsic knowledge of quantum mechanics, physics, biology, or economics.
Instead, it serves as a powerful phrasing engine—a source of deterministic, structured unpredictability around which domain-specific rules can be wrapped. Its value lies in providing a computationally traceable method for driving probabilistic models. The researcher or physicist defines the laws and probability distributions of their system; FPS-R provides the deterministic “dice rolls” to explore the consequences of those laws in a perfectly repeatable manner.
The scientific validity of any resulting simulation, therefore, depends entirely on the quality of the expert’s model, not on FPS-R itself. This introduces an element of artistry and skill, where the researcher’s ability to tune FPS-R’s phrasing to match observed phenomena determines the fidelity of the simulation.
In this paradigm, FPS-R is not used to predict a single future, but to reliably reconstruct the intricate pathways that create any possible future within a given model, over and over again.
Note: The following describes a potential application of FPS-R as a computational tool for building and analysing models of quantum-like systems. It is not a claim about simulating quantum reality itself.
The core challenge in simulating quantum systems is their inherent probabilistic nature. Using standard random number generators makes experiments non-repeatable, rendering the study of how complex patterns emerge from simple rules nearly impossible. This is where FPS-R can offer a unique advantage.
Instead of a “deterministic oracle,” think of FPS-R as a deterministic pseudo-random source. It allows a researcher to build a model where every probabilistic event—every “quantum jump”—is driven by a predictable, repeatable number.
rand(), the simulation calls an FPS-R function. The output (a float from 0.0 to 1.0) is used to select an outcome from the probability distribution defined by the model’s rules.FPS-R does not simulate quantum mechanics. It provides a robust, traceable framework for building and stress-testing the mathematical models that scientists create to understand them.
FPS-R enables a form of epistemic phrasing: a new way to ground probabilistic systems in determinism, turning the chaos of emergence into a reliable, readable text in order they may be studied and that new understandings and insights may form.
FPS-R can possibly pave a new way to study a probabilistic system by supplying determinism as its core.
By re-contextualizing the frame input from a measure of time to a coordinate in space (x, y, z), FPS-R evolves into a topological phrasing system. It can describe large-scale emergent phenomena over vast spatial and temporal epochs, all without storing massive simulation data.
Here, the challenge here is for domain users to provide the context to match the hold periods, space and durations to match observed distances or time periods. What then follows is pacing, phrasing, and probable unpredictability that FPS-R brings to the cosmic table.
hold state can represent a contiguous rock stratum or biome, while a jump signifies a sharp, natural boundary to a different formation. SM can model organic erosion patterns, while TM can represent cyclical geological eras.Many biological systems are governed by complex, probabilistic interactions. FPS-R can provide the deterministic engine needed to explore their emergent behaviours.
Modeling chaotic systems like atmospheric turbulence or ocean currents suffers from the same reproducibility problem. FPS-R brings a structured traceability enabling a historical timeline to developing and modelled conditions. Different instances can be stacked upon each other to form interconnected systems that accumulate or cancel each other out, and the results will still be deterministic and replayable.
Human behaviour, especially in large groups, is a classic emergent system based on individual, probabilistic decisions. Multiple instances of FPS-R can drive individual agents, and keep the system deterministic, and study the emerging behaviour of the group.
In the end, FPS-R is not just a tool for generating behaviour—it is a grammar of time. It doesn’t simulate noise. It phrases emergence. And the more fluently we learn to read its parameters, the more expressive and explainable our systems become.
Whether shaping synthetic motion, decoding emotional rhythm, or reconstructing plausible memory, FPS-R offers not the right answers, but the right space in which to ask better questions.
Phrasing isn’t about control. It’s about timing. And through timing, we see not just what happens—but how something becomes itself.
FPS-R began as a modulation engine. It has become a language of behavioural emergence.
At its core, FPS-R offers a new vocabulary for a long-neglected modality: the expressive logic of random-move-and-hold. Where most systems focus on decisions, FPS-R focuses on how decisions unfold—through rhythm, drift, hesitation, and momentum.
In its most expanded form—with rich capsule libraries, intuitive tools, and a growing community—FPS-R unlocks two powerful paradigms:
Generative Expression: Latent token drift enables procedural systems to evolve identity over time, crafting behaviours that breathe, hesitate, and resolve with nuance.
behavioural Inference: Temporal anchoring allows analysts and agents to fit observed phenomena to structured phrasing, enabling plausible reconstruction of past events and resonant extrapolation into the future.
These aren’t features—they’re foundations. FPS-R supplies:
From game design to system forensics, expressive UI to cognitive simulation, FPS-R expands what procedural systems can mean. It invites a new grammar of emergence—not just a way to make things move, but a way to understand how and why they do.
In a world of continuous action, FPS-R gives shape to what holds still—
and meaning to what changes with rhythm.