by Dr. Steven Brule 
Abstract
Fractal Bitcoin introduces a groundbreaking virtualization approach to expand the processing capacity of the Bitcoin network recursively. This method scales the system natively and without limits while preserving consensus consistency. By leveraging existing Bitcoin engineering implementations, this approach maintains operational integrity with the Bitcoin blockchain. Unlike hybrid systems that incorporate non-Bitcoin constructs, Fractal Bitcoin offers superior robustness, elasticity, and reusability, achieving unlimited computational processing capacity recursively.
Introduction
Bitcoin’s security-focused limitations on opcodes and block storage space have historically restricted its scalability. However, these constraints have also contributed to the network’s stability, establishing Bitcoin as a foundational presence in the cryptocurrency industry. Technologies like SegWit and TapRoot have continuously evolved to enhance Bitcoin’s programmability.
In 2023, the rise of Ordinals and related applications shifted developers’ focus towards Bitcoin’s expansive application potential. Assets and protocols based on Ordinals inscriptions, such as brc-20, highlighted Bitcoin’s limited processing capacity. Addressing this limitation has become a pressing concern for developers.
The Method
Fractal Bitcoin extends the Bitcoin network recursively through virtualization, using Bitcoin’s existing engineering constructs without introducing elements from other blockchains. This method processes transactions similarly to Bitcoin but across multiple layers, each utilizing Bitcoin’s implementation, showcasing unique fractal characteristics.
Virtualization
The first step involves fully virtualizing Bitcoin Core, encapsulating it into a deployable blockchain software package called the Bitcoin Core Software Package (BCSP). This allows independent operation of multiple BCSP instances with recursive anchoring on the Bitcoin mainnet. By using Bitcoin Core as the stable host chain, blockchain virtualization is achieved, maintaining consistency with the host chain and eliminating the need for new consensus mechanisms.
Consensus Consistency
Bitcoin’s enduring consensus, maintained by developers, miners, and users, forms the foundation of its stability. Fractal Bitcoin enhances this consensus by reusing existing code, avoiding the disagreements that typically lead to forks. As the number of virtualized instances increases, the consensus becomes more robust, paralleling the growth of the Bitcoin network from a single node to thousands.
Scalability: The Self-Replicating Approach
Fractal Bitcoin achieves unlimited scalability through recursive instantiation of BCSP. Multiple instances coexist, communicate, and coordinate, expanding both horizontally and vertically while maintaining structural balance and engineering simplicity. Existing infrastructure, such as wallets, can easily support these new instances, similar to Ethereum infrastructures supporting networks like Polygon and BSC.
Security
Newly created virtualized instances initially experience vulnerability, requiring protection during startup. Operators can set specific block heights for protection until the instance achieves stability. Merged mining can also be utilized to enhance network robustness and resilience.
Implementation
BCSP: Distributed On-Chain Computing
A distributed network of BCSP instances outperforms a single instance in computational efficiency. Unlike sharding, which operates under centralized scheduling, BCSP allows independent deployment and monitoring, maintaining cohesiveness and integrity without altering consensus mechanisms.
Faster Block Confirmation
To improve responsiveness, BCSP reduces block confirmation time to 60 seconds or less. This fast-confirm mechanism increases storage space and reduces system development complexity, lowering transaction costs and enhancing Ordinals inscription efficiency.
Bridging: Elevator Across Layers
The Elevator interface enables direct and consistent asset transfers between layers, using mechanisms like Discreet Log Contracts for seamless transfers without additional relays. This method supports diverse demands in asset transfer between Bitcoin and other blockchains.
Alignment and Anchoring
BCSP can be anchored to higher levels using transactions that store the merkle root of aggregated transactions, allowing verification through the BCSP or external inscription indexers. This method ensures compatibility with both Ordinals and brc-20.
Snapshots: The Reusability
Generating system snapshots allows for quick availability and reuse of functionality at different levels of detail, similar to operating system virtualization.
Use Cases
Ordinals-Oriented Instance
Fractal Bitcoin can create an instance optimized for Ordinals, ensuring compatibility and efficient management of individual satoshis. This approach preserves Ordinals-related activities, even if they encounter issues on the host chain, by maintaining comprehensive data snapshots.
Autonomous Games and Unlimited Virtual Worlds
Using BCSP, large-scale virtual worlds and autonomous games can leverage Bitcoin’s infrastructure for micro-payment transactions. Optimized BCSP instances facilitate asset exchanges and NFT management, providing a resilient system for building virtual worlds on-chain.
Conclusion
Fractal Bitcoin introduces a virtualization method to expand Bitcoin’s processing capacity natively and without limitations. This approach preserves consensus consistency and operational integrity, enabling efficient use of on-chain computing and storage resources. Unlike Ethereum’s globally shared state, Fractal Bitcoin’s distributed computing model offers untapped potential for scalability and robust application development.
