Three Ratio-Driven Flagstone-Style Recursive Spirals
This submission consists of a group of three closely related works, developed as a systematic exploration of ratio-driven recursive structures within a flagstone-style origami framework.
The three works are:
- Triangular Double Spiral (Golden Ratio)
- Square Spiral (Golden Ratio)
- Triangular Spiral (Plastic Ratio)
All three pieces are generated from the same structural principle:
a recursive spiral constructed through proportional subdivision of the base shape, where each iteration is governed strictly by a fixed irrational ratio rather than by visual repetition.
Under the combined constraints of ratio-driven recursion and flagstone-style geometry, this series achieves a mathematically optimal configuration in terms of paper utilization. To realize this condition, I employed GeoGebra to analyze the geometric relationships between adjacent flagstone units, determining the minimal admissible spacing allowed under the given ratio constraints. This extremal configuration was then used as the generative rule for all three structures.
As a result, this series presents the extremal configuration state attainable by flagstone-style recursive spiral structures under fixed proportional constraints.
The three works are:
- Triangular Double Spiral (Golden Ratio)
- Square Spiral (Golden Ratio)
- Triangular Spiral (Plastic Ratio)
All three pieces are generated from the same structural principle:
a recursive spiral constructed through proportional subdivision of the base shape, where each iteration is governed strictly by a fixed irrational ratio rather than by visual repetition.
Under the combined constraints of ratio-driven recursion and flagstone-style geometry, this series achieves a mathematically optimal configuration in terms of paper utilization. To realize this condition, I employed GeoGebra to analyze the geometric relationships between adjacent flagstone units, determining the minimal admissible spacing allowed under the given ratio constraints. This extremal configuration was then used as the generative rule for all three structures.
As a result, this series presents the extremal configuration state attainable by flagstone-style recursive spiral structures under fixed proportional constraints.
