Parametric Curve Families

Overview

Each square is parameterized by an index *i* which defines its rotation as θ = 2π5i and its position along a circular trajectory with radius modulated by sin(i)⋅sin(i^∘). The size of the square is not constant but dynamically scaled using the expression tan(θ) · cos²(θ) · π² · 6tan(θ) · cos²(θ) · π² · 6, introducing controlled divergence in shape as the angle approaches singularities. By embedding this logic into affine transformations, I was able to simulate both orbital motion and internal expansion simultaneously, allowing pure math to dictate structure, symmetry, and disorder within a single evolving visual language.

This work explores the interplay between parametric geometry and affine transformation by generating a sequence of rotated and translated squares governed by trigonometric functions. I constructed each square using an evolving angular parameter and computed its scale from a composite function involving tangent, cosine, and pi constants. This produces a family of curves where each square's size reflects subtle nonlinear distortions. The rotational symmetry is reinforced by a uniform angular step, while translation is constrained along the horizontal axis through a sinusoidal modulation. The cumulative effect is a densely interlaced structure where geometry behaves like a wave collapsed into architecture.

You can find my code repository here.