page_title: John von Neumann
section_title: Cellular automata, DNA and the universal constructor
hierarchical_section_title: John von Neumann / Computing / Cellular automata, DNA and the universal constructor
caption_attribution_description: English: The Nobili-Pesavento self-replicator, with a daughter copy in the process of making a grand-daughter copy. The automaton uses the 32-state extended John von Neumann rules, based on his work on universal constructors and self-reproducing automata.
context_page_description: John von Neumann was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. Von Neumann was generally regarded as the foremost mathematician of his time and said to be "the last representative of the great mathematicians"; he integrated pure and applied sciences.
  Von Neumann made major contributions to many fields, including mathematics, physics, economics, computing, and statistics.
  He was a pioneer of the application of operator theory to quantum mechanics in the development of functional analysis, and a key figure in the development of game theory and the concepts of cellular automata, the universal constructor and the digital computer.
  Von Neumann published over 150 papers in his life: about 60 in pure mathematics, 60 in applied mathematics, 20 in physics, and the remainder on special mathematical subjects or non-mathematical ones. His last work, an unfinished manuscript written while he was in the hospital, was later published in book form as The Computer and the Brain.
  His analysis of the structure of self-replication preceded the discovery of the structure of DNA.
context_section_description: Von Neumann's rigorous mathematical analysis of the structure of self-replication (of the semiotic relationship between constructor, description and that which is constructed), preceded the discovery of the structure of DNA.
  Von Neumann created the field of cellular automata without the aid of computers, constructing the first self-replicating automata with pencil and graph paper.
  The detailed proposal for a physical non-biological self-replicating system was first put forward in lectures von Neumann delivered in 1948 and 1949, when he first only proposed a kinematic self-reproducing automaton. While qualitatively sound, von Neumann was evidently dissatisfied with this model of a self-replicator due to the difficulty of analyzing it with mathematical rigor. He went on to instead develop a more abstract model self-replicator based on his original concept of cellular automata.
  Subsequently, the concept of the Von Neumann universal constructor based on the von Neumann cellular automaton was fleshed out in his posthumously published lectures Theory of Self Reproducing Automata. 
  Ulam and von Neumann created a method for calculating liquid motion in the 1950s. The driving concept of the method was to consider a liquid as a group of discrete units and calculate the motion of each based on its neighbors' behaviors.  Like Ulam's lattice network, von Neumann's cellular automata are two-dimensional, with his self-replicator implemented algorithmically. The result was a universal copier and constructor working within a cellular automaton with a small neighborhood (only those cells that touch are neighbors; for von Neumann's cellular automata, only orthogonal cells), and with 29 states per cell. Von Neumann gave an existence proof that a particular pattern would make infinite copies of itself within the given cellular universe by designing a 200,000 cell configuration that could do so.
  Von Neumann addressed the evolutionary growth of complexity amongst his self-replicating machines. His "proof-of-principle" designs showed how it is logically possible, by using a general purpose programmable ("universal") constructor, to exhibit an indefinitely large class of self-replicators, spanning a wide range of complexity, interconnected by a network of potential mutational pathways, including pathways from the most simple to the most complex. This is an important result, as prior to that it might have been conjectured that there is a fundamental logical barrier to the existence of such pathways; in which case, biological organisms, which do support such pathways, could not be "machines", as conventionally understood. Von Neumann considers the potential for conflict between his self-reproducing machines, stating that "our models lead to such conflict situations", indicating it as a field of further study.
  The cybernetics movement highlighted the question of what it takes for self-reproduction to occur autonomously, and in 1952, John von Neumann designed an elaborate 2D cellular automaton that would automatically make a copy of its initial configuration of cells. The von Neumann neighborhood, in which each cell in a two-dimensional grid has the four orthogonally adjacent grid cells as neighbors, continues to be used for other cellular automata. Von Neumann proved that the most effective way of performing large-scale mining operations such as mining an entire moon or asteroid belt would be by using self-replicating spacecraft, taking advantage of their exponential growth.
  Von Neumann investigated the question of whether modelling evolution on a digital computer could solve the complexity problem in programming.
  Beginning in 1949, von Neumann's design for a self-reproducing computer program is considered the world's first computer virus, and he is considered to be the theoretical father of computer virology.
caption: The first implementation of von Neumann's self-reproducing universal constructor.[165] Three generations of machine are shown: the second has nearly finished constructing the third. The lines running to the right are the tapes of genetic instructions, which are copied along with the body of the machines.
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