numeralmakes

Numeralmakes is a term used in theoretical puzzles and metamathematical discussions to describe a family of numbers generated by digit-based production rules. It is not part of standard mathematical nomenclature but serves as an illustrative construct for exploring how local transformations of digits affect the global structure of numbers.

A numeralmake is specified by three components: a base b (typically 10), a digit-transform function D that assigns to each digit a nonnegative integer, and a composition rule C that combines those outputs into a final number. Starting from a seed n, one applies D to each digit of n and then uses C to assemble the transformed digits. Repeating the process yields the numeralmake orbit of n.

Example. Let base be 10, D map each digit to the number of segments in a seven-segment display, and C be concatenation. In this scheme digits 0–9 map to 6, 2, 5, 5, 4, 5, 6, 3, 7, 6 respectively. Starting with 23, D(2)=5 and D(3)=5, giving 55. Applying D to 55 yields 5 and 5, so the next term is 55 again. Thus 55 is a fixed point of this numeralmake rule.

Variations of D and C produce different behavior. Some configurations yield cycles of length greater than 1, while others drive numbers toward fixed points or toward unbounded growth. The framework is primarily used for illustrating digit-level dynamical systems and for crafting educational puzzles about orbit behavior.

See also: digit dynamical system, recreational mathematics, sequence generation.

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