Multi-User Interactive Scenario?

MDWA - easily associated with single user, progressive storytelling…
No no. This interaction scenario using superposition of states create new methodology to approach N simultaneous user interaction

Multi-User Scenario (M Users) 
Wave 중첩? 
Just like wave interferecen – different user interactions interfere to each other?
Quantum State과 같이?
두개 이상 유저 있을 경우 → 이 유저 서로 다른 State Command하는 인터랙션 (상태 충돌)
Assume Multi-Channel Output (N Screens)
Single Channel Output의 State는 Given M Eigenvalues 사이에서 Oscillation 
Randomly: 어쩔땐 User 1 이 Insist하는 State1, 어쩔땐 User2의 State2 사이에서 양자적으로 움직임 
Superposition of states
Nondeterministic Computing
이때 State 별 Transition Probability는 Markov Chain 적으로? Need more research
Multi-Channel Perspective에서 봤을때: 마치 바삐 움직이는 도시처럼, 하나의 생태계처럼, 각 Channel이 Random State 사이 움직이면, 전체적으로는 모든 Channel 상 State Randomly 움직이는게… 마치 기차역 플랫폼처럼! 플랫폼 아트적으로 움직인다!
State-based Approach가 Backing 되어야
즉 각 채널 AV Output은 State-based, not progressive
NJP!

1. Conceptual Overview
Your approach envisions a multi-user, multi-channel interactive system in which:
M users each provide a “state command” (a desired state or input).
The system, modeled as a graph or network, dynamically oscillates between these different states.
Each channel (of the N channels/screens) does not follow a linear narrative but instead displays an output state that is determined probabilistically—akin to how a quantum system exists in a superposition of eigenstates before “collapsing” to one state.
The transition between states is conceptualized in terms of Markov Chain dynamics, where the probability of moving from one state to another is determined by user influence, potentially leading to emergent, wave-like oscillations across the channels.
This idea is meant to evoke an image of a bustling, ever-shifting “urban” ecosystem (or train station platform) where no single narrative is fixed; instead, each output is an emergent snapshot of a much larger, invisible system (the hyperobject).

2. Theoretical Underpinnings
Graph/Network Theory
Modularity and Subgraph Swapping:
 Your idea that one can “swap” a subgraph (a subsection of the system) with another, while keeping the overall structure constant, is well rooted in graph grammars (see Rozenberg’s work). This modularity allows the system to remain flexible and adaptive, and it supports the idea that user inputs (nodes) can be rearranged dynamically.
Dynamic Network Behavior:
 In multi-agent systems and dynamic networks, it is common to see oscillatory behavior emerge from local interactions—especially when multiple inputs vie for influence. Here, the notion of each screen’s state oscillating among the “eigenvalues” defined by M users aligns with how networks can exhibit collective dynamics, with local perturbations causing widespread shifts.
Quantum Mechanics and State Superposition
Quantum State Analogies:
 The comparison to quantum states is metaphorical but apt: just as a quantum system can exist in a superposition of eigenstates until measured, your system’s output on each channel is not fixed but oscillates between different user-defined states. Once a “measurement” (or output) occurs, it may “collapse” into one state, only to later be influenced by other inputs.
Eigenvalues and Oscillation:
 In quantum mechanics, eigenvalues represent the possible outcomes of a measurement. If we think of each user’s command as contributing an “eigenvalue,” then the observed state on a channel is an emergent property determined by the competing influences—a concept which resonates with the idea of a Markov Chain describing the probability of transitions between states.
Stochastic Processes and Markov Chains
Probabilistic State Transitions:
 Modeling the system’s transitions using a Markov Chain is theoretically sound. In a Markov model, the next state depends only on the current state (memorylessness), and transitions occur with specific probabilities. This can be used to simulate how a channel might randomly shift between different user-influenced states.
Emergent Dynamics:
 In many stochastic systems (such as inventory control or queuing networks in industrial engineering), local random interactions lead to emergent global behavior. This mirrors your vision: individual users’ actions (inputs) produce an unpredictable yet statistically governed evolution in each channel’s output.
Industrial Engineering and Systems Modeling
Multi-Agent and Multi-Channel Systems:
 In industrial engineering, especially in supply chain management, complex systems are often modeled as networks where multiple inputs (orders, demands) affect outputs (production, delivery). The concept of cascading failures and feedback loops in supply chain networks is similar to how user inputs might lead to unpredictable transitions in your system.
Decentralized Control:
 Just as modern manufacturing systems may operate with distributed control (each machine or process making local decisions that contribute to overall system behavior), your model envisions a system where no single user has complete control—the collective influence shapes the overall state. This is a hallmark of decentralized, self-organizing systems.

3. Evaluation of Validity
Strengths
Interdisciplinary Soundness:
 Your model borrows robust ideas from graph theory, quantum analogies, and stochastic processes to create a system that is both dynamic and emergent. It aligns with contemporary theories of distributed systems and hyperobjects.
Emergent Behavior:
 The idea that outputs oscillate among multiple states based on user input captures the essence of emergent phenomena – where local interactions produce global patterns that are not pre-scripted. This is a key aim of many system art projects.
Reflective of Contemporary Digital Interactions:
 The model echoes how modern digital platforms operate – with users influencing content in a way that is often non-linear and unpredictable (e.g., viral trends, rapidly shifting social media content).
Challenges and Considerations
User Interpretability:
 While mathematically elegant, such a probabilistic and quantum-inspired model might feel too arbitrary to users if they cannot discern how their inputs affect the system. It will be important to design feedback mechanisms so that users have a sense of agency.
Balancing Randomness and Control:
 If state transitions are too random, users may feel they have little control. Conversely, if the model is too deterministic, it loses the emergent, hyperreal quality you seek. A delicate balance must be struck—possibly by incorporating adaptive probabilities that evolve based on sustained user input.
Computational Complexity:
 Implementing real-time Markov models across multiple channels (N screens) with numerous users (M users) is non-trivial. Efficient algorithms and possibly distributed processing may be required to ensure the system remains responsive.
Conceptual Clarity:
 The quantum and wave analogies are compelling but can be easily misunderstood if not well contextualized. Users need a minimal, intuitive explanation (or visual metaphor) for how their actions contribute to the state dynamics without overwhelming them with technical detail.

4. Conclusion
Your multi-user, multi-channel, state-based interactive system is a promising experimental model that integrates:
Graph Theory and Network Science: For modularity and dynamic interconnection.
Quantum Analogies: For illustrating non-deterministic, superpositional state changes.
Markov Chains: As a formal method for modeling probabilistic state transitions.
Industrial Engineering Principles: For understanding decentralized control and emergent phenomena in complex systems.
This approach is conceptually valid and rich in theoretical support. It captures the emergent, non-linear behavior central to system art, while also critiquing the idea that our interactions are merely deterministic progressions. The challenge lies in designing the interface and feedback loops so that users perceive meaningful agency amid the inherent randomness. With careful calibration and an emphasis on intuitive interaction (e.g., sliding gestures that mimic continuous, fluid motion), your model can vividly simulate an environment where user inputs “interfere” like waves on a busy urban platform, reflecting both individual commands and the collective, emergent state of the system.
Overall, the model is an excellent application of interdisciplinary theories in system art—merging insights from mathematics, computer science, and industrial engineering to build a dynamic, interactive artwork that reflects the complexity and unpredictability of contemporary social systems.