On this site are recent technical papers, plus one old one.

#### The H-Machine Series

This pair of papers began with *Chaos and Complexity*, which posits new definitions of chaos with a philosophical interpretation, and provides a basis for the hypergraph-based H-Machine. The other paper describes the H-Machine in detail, provides an implementation, and reports the results of some experiments.

##### Chaos and Complexity

** Abstract** Relations are explored and developed among the mathematical theory of chaos, models of software, and philosophical characterizations of chaos and complexity. A generalization of sensitivity and transitivity, termed model jumping, is defined and developed, and used to characterize behavior observed in software systems and more general physical and humanistic situations. The generalizations and characterizations are tied together via a simple computational model based on graph transformation.

**Chaos and Complexity Pdf**

##### The H-Machine

** Abstract** The H-Machine is a hypergraph-based language and interpreter, based on rule matching by hypergraph isomorphism. Rules are part of the hypergraph being constructed, and can be matched and modified as can other data, thus forming a complete meta-system. The H-Machine language is extremely simple, yet can express a wide range of data structures and computations, with inherent parallelism. The matching system allows a full range of expression of recursive relations, implicit iteration, and, via meta-rules, a modular way to describe computation at a high level.

Data and rules have a simple graphical interpretation which offers good visibility into the resulting structures. Examples illustrate both data and rule structures, derived data flow graphs, cellular automaton matrices, ancillary relations, and rules – predicate subgraph, edges to be added, edges to be deleted — within a single graphical model. The Graphviz toolkit is used for rendering. Implementation is briefly described, with links to code and a gallery of generated H-Machine runs.

**The H-Machine (abridged) Pdf**

**The H-Machine (full paper) Pdf**

#### Other Recent Papers

**Aunt Betty’s Clock** describes getting Aunt Betty’s circa-1900 clock to work, and analyzes aspects of its operation and accuracy.

**Self-Descriptive Number Fixed-Point Function** is a formulation of a fixed point on a decimal self-descriptive number, and I believe is noteworthy in its use of Fermat’s Little Theorem.

**Listening to the Riemann Zeta Function**is an exercise in sound generation and a harmonic analysis of the Zeta and related functions.

#### Something Old

**An Architecture for the Execution of Applicative Languages (1979)** is a scan of an old paper. While technically it may be of interest, the main reason to post it is to note the old-fashioned manner of its production: hand-drawn pictures, math symbols hand-written into the final typed paper, and so forth. Unlike school projects of only a few years earlier, this was edited and and formatted on a computer, anyway, a Prime time sharing system.

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