**Kinematic
Self-Replicating Machines**

**©
2004 Robert A. Freitas Jr. and Ralph C. Merkle. All Rights Reserved.**

Robert A. Freitas Jr., Ralph C. Merkle, *Kinematic Self-Replicating Machines*,
Landes Bioscience, Georgetown, TX, 2004.

**5.9 Brief Mathematical
Primer on Self-Replicating Systems**

Given the vastness of the replicator design space (Section 5.1.9), it is impossible in the limited space available here to attempt even a balanced summary of the mathematics of self-replication that might apply to each class of replicator. Each of the 137 design dimensions described in Section 5.1.9 requires a painstaking mathematical analysis whose full specification lies considerably beyond the scope of this book. We will describe here only a few of the most basic concepts, including Fibonacci numbers (Section 5.9.1), exponential population growth strategies (Section 5.9.2) and limitations (Section 5.9.3), and finally the general performance of convergent assembly manufacturing systems (Section 5.9.4), power law scaling (Section 5.9.5), and design tradeoffs related to nanofactory process specialization (Section 5.9.6).

Last updated on 1 August 2005