Mathematical Art Generator
Explore the beauty of geometry. Espiralito creates art from mathematical principles — spiral curves, rotational symmetry, and algorithmic color mapping.
Create Mathematical ArtSpiral Geometry
Each artwork follows a spiral path — shapes positioned along a curve whose radius increases with each step. The math behind the spiral determines its character.
Rotational Symmetry
Set symmetry from 1-fold to 16-fold. Higher symmetry creates mandala-like patterns where the spiral arm is duplicated and rotated around the center.
Geometric Shapes
Choose from seven geometric primitives: circles, squares, triangles, pentagons, hexagons, stars, and diamonds. Each shape adds a different mathematical quality to the composition.
Color Mapping
Color palettes map element position to hue. Rainbow mode uses cyclic hue rotation. Complementary palettes use opposite hues. Custom palettes interpolate through hand-picked color stops.
Noise-Based Variation
Simplex noise adds organic variation to the spiral's radius. This mathematical function produces smooth, continuous randomness that mimics natural patterns.
Perspective Transformations
The 3D effect applies rotation and perspective projection to the 2D spiral, creating the illusion of depth through mathematical coordinate transformation.
The Mathematics Behind the Art
Every pixel in an Espiralito artwork is calculated from mathematical formulas. Here are the core concepts:
Spiral Equations
The base spiral places elements at positions defined by:
- Radius:
r = i × spacing × scale, whereiis the element index - Angle:
θ = i × 15° + (time × speed), creating the spiral's angular progression - Position:
x = cx + r × cos(θ),y = cy + r × sin(θ)
The constant 15° per element creates a tight spiral. Varying the spacing and scale parameters changes the spiral's density and extent.
Rotational Symmetry
When symmetry is set to n, each spiral element is duplicated n times, rotated by 360°/n × k for k = 0, 1, ..., n-1. This creates patterns with n-fold rotational symmetry — the same visual appearance after rotating by 360°/n.
Mandala-like patterns emerge at high symmetry values (8–16), while lower values (2–4) create more asymmetric, flowing compositions.
Simplex Noise
Ken Perlin's Simplex noise algorithm generates smooth, continuous random values in any number of dimensions. Espiralito uses 2D simplex noise with the seed-derived PRNG to vary the spiral's radius at each step, creating organic, non-repeating distortions.
Color Theory in Algorithmic Art
Color assignment follows mathematical rules:
- Rainbow: hue =
(i × 15 + time) mod 360— full spectrum rotation - Monochromatic: fixed hue with lightness variation via sine function
- Complementary: hue alternates between two opposite colors
- Custom: RGB interpolation through a gradient defined by color stops
The Golden Ratio and Spirals
While Espiralito uses a uniform angular increment (15°) rather than the golden angle (~137.5°), the relationship between spacing and scale can approximate golden spiral proportions. The golden ratio (φ ≈ 1.618) appears in many natural spirals — from nautilus shells to galaxy arms — and understanding this connection enriches the appreciation of spiral art.
Mathematical Art in the Gallery
Explore Mathematical Beauty
Tweak the equations. Change the parameters. See what mathematics looks like as art.
Open the Generator →