From Deterministic Individuals to Emerging Complex Systems: Understanding the Differences and Relationships between CAS and Turing Machine M Using Bitcoin as an Example The Turing machine (M), as the cornerstone of computational theory, represents an abstraction of the computing power of a single deterministic individual. Complex Adaptive Systems (CAS) provide a framework for understanding systems composed of numerous interacting individuals that exhibit emergent behavior. This article aims to compare the core differences between CAS and Turing machines and explain their relationship. Finally, taking Bitcoin as an example, this article illustrates how Bitcoin, a decentralized CAS, emerged through complex interactions from seemingly deterministic "Turing like" individuals, including human individuals who construct transactions as a type of "Turing machine". Turing machine (M): isolated deterministic computational model A Turing machine is a theoretical computational model whose core is an independent entity that follows deterministic rules. Its composition includes a finite state controller, a read-write head, an infinitely long paper tape, and a determined transfer function. For a given input, the Turing machine calculates strictly according to its preset rules, producing a unique and deterministic output. It is an isolated system that does not involve interaction with other individuals or adaptation to the environment. The focus of Turing machines lies in the computational power and computability theory of individual entities. Complex Adaptive Systems (CAS): The Whole Behavior of Interaction Emergence Unlike Turing machines, CAS focuses on systems composed of a large number of autonomous individuals who, through local interactions, exhibit complex behaviors as a whole. The key features of CAS include: Composition: A large number of interacting individuals (Agents), who may have different attributes and behavioral rules. Interaction: There are local and complex interactions between individuals, and information and influence propagate in the network. Behavior: The macroscopic behavior of a system is emergent and cannot be simply predicted from the superposition of individual behaviors, often exhibiting nonlinear, self-organizing, and other characteristics. Adaptability: The system as a whole can adjust its structure and behavior according to changes in the environment. Control: CAS is usually decentralized and does not have a single controlling entity. The Difference and Relationship between Turing Machine M and CAS: Micro Certainty and Macro Complexity There are significant differences in research objects and methods between Turing machines and CAS: Turing machines study the computational limits of a single deterministic individual, while CAS studies the macroscopic complex behavior generated by the interaction of a large number of individuals. However, individuals in CAS can be considered as basic units with certain "Turing like" characteristics. These individuals follow their own rules and protocols, similar to the transfer function of a Turing machine. The key difference is that CAS places these "Turing like" individuals in an interconnected network, and through a large number of nonlinear interactions between them, as well as interactions with the environment, emerges complex behaviors and functions that cannot be achieved by a single Turing machine individual. Therefore, CAS can be seen as a system composed of a large number of individuals who follow local deterministic rules, and its macroscopic behavior is the non trivial result of the interaction between these local deterministic behaviors. Bitcoin: From Turing like Individuals to Emerging Decentralized CAS Bitcoin provides a concrete example of how to emerge as a decentralized CAS through complex interactions, starting from seemingly deterministic "Turing like" individuals, including humans, who construct transactions as a type of "Turing machine" UTXO: Deterministic State Transition Unit. Each UTXO can be regarded as a state unit that follows Bitcoin trading rules, and its transition is constrained by strict cryptographic rules, similar to a "mini Turing machine" that performs deterministic state transitions. Miner: A "mini Turing machine" that executes deterministic PoW algorithms. Each miner is an entity that executes PoW algorithms and can be seen as a "mini Turing machine" that receives transaction information, performs hash calculations, and attempts to find block hashes that meet difficulty objectives. The behavior of miners follows clear algorithmic rules and is deterministic. The asymmetry of PoW (difficult to solve, easy to verify) is the key to emerging network security. Blockchain: Deterministic Verification and Record Structure As a distributed ledger for recording transactions and blocks, the verification and linking process of blockchain follows strict protocol rules and is a deterministic data structure. The emergence of Bitcoin: individual interaction and asymmetry The macro characteristics of Bitcoin are not independently generated by any single component, but arise from the interaction of the following factors: The interaction of a large number of "Turing like" individuals: The process of constructing transactions by human individuals behind UTXO can be regarded as a computing process of a type of "Turing machine", consisting of a large number of distributed TX transaction construction processes to form a pool of transactions to be verified; Numerous miners compete as "mini Turing machines" to generate blocks based on PoW rules; Network nodes follow the blockchain protocol for verification and synchronization. The key role of asymmetry: The computational asymmetry of PoW (NP solving, P-verification) ensures the security of the network; The relative simplicity of transaction verification ensures the efficiency of the network. It is the large-scale interaction between these deterministic individuals (the transaction construction process behind UTXO, miners following PoW rules, and nodes following protocols) that has given rise to the unique features and attributes of Bitcoin as a decentralized, trustless digital currency system. The case of Bitcoin demonstrates that individuals following local deterministic rules can exhibit global and adaptive complex behaviors through complex networked interactions, which is the core idea of CAS and reveals the profound relationship between deterministic individuals and emerging complex systems.