Prime Geometry: A Deterministic Geometric Representation of Prime Numbers

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Prime Geometry: A Deterministic Geometric Representation of Prime Numbers

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A collection of computational visualizations exploring deterministic geometric constructions generated from integer sequences. The images illustrate how simple local turning rules based on prime and composite numbers produce complex global geometric structures.

This Video illustrates a geometric construction generated by the Prime Geometry algorithm.

Starting from an initial position and tangent direction, each processed integer determines the orientation of the next circular arc according to a deterministic turning rule. The connected arcs form one continuous geometric trajectory.

The color gradient represents the chronological progression of the construction, beginning in dark blue and ending in dark red.

The red point marks the starting position of the construction.

The blue square marks the final position of the trajectory after all integers have been processed.

The yellow cross indicates the geometric centroid (center of mass) of the complete trajectory. As the construction grows, this centroid gradually stabilizes and serves as a global geometric reference.

The figure illustrates how deterministic local rules applied to integer sequences can generate complex global geometric structures. Different turning angles produce different geometric patterns while the construction remains completely deterministic.

This visualization is intended as a computational exploration of geometric representations generated from integer sequences. It does not claim a new theorem, a new primality test, or a mathematical proof concerning the distribution of prime numbers.

The complete implementation, source code, and documentation are available in the accompanying GitHub repository.

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