About

This Abstract Art Generator utilizes stochastic processes and procedural algorithms to create unique digital compositions. Unlike static image banks, this tool renders fresh pixels in real-time using mathematical functions to determine shape, placement, and color blending.

The engine leverages Stochastic Geometry. By defining probability distributions for vertex coordinates and control points, the system generates non-deterministic outcomes that maintain aesthetic coherence. The optional Noise filter adds a granular texture, simulating physical media by introducing variance to the pixel buffer, effectively dithering gradients to prevent banding.

Whether for web backgrounds, print media, or digital wallpapers, the output is rendered at high density to ensure sharpness on Retina displays. The logic incorporates Alpha blending modes to create depth, simulating layers of light and pigment.

Formulas

The Fluid mode relies on the Cubic Bézier Curve formula to generate smooth, organic paths. The position B at time t is calculated by interpolating between four control points:

B(t) = (1−t)³P₀ + 3(1−t)²tP₁ + 3(1−t)t²P₂ + t³P₃

Legend:

B(t) = Coordinate of the curve at percentage t (0 to 1).
P₀, P₃ = Start and End anchors.
P₁, P₂ = Directional control handles.

Reference Data

Shape Topology	Psychological Association	Mathematical Basis	Complexity Cost
Circle / Ellipse	Unity, Wholeness, Infinity	x² + y² = r²	Low
Triangle / Polygon	Stability, Tension, Conflict	Linear Interpolation (Lerp)	Low-Mid
Bézier Curve	Fluidity, Motion, Calm	Bernstein Polynomials	High
Fractal Noise	Chaos, Nature, Texture	Recursion / Random Walk	Mid
Grid / Matrix	Order, Logic, Structure	Cartesian Coordinates	Low

Frequently Asked Questions

Yes. The images are generated client-side in your browser. You own the copyright to the specific output you generate, and it is royalty-free.

The generator renders at a base resolution of 1920x1080 pixels (Full HD). However, on high-DPI (Retina) screens, it may render at double density (3840x2160) for sharpness.

Higher complexity increases the number of geometric iterations (n). If n > 500, the browser's rendering engine requires more processing time to calculate path intersections and alpha blending.

The texture setting applies a noise filter over the canvas. It iterates through the pixel buffer array, modifying the RGB channels of random pixels by a small delta factor to simulate grain.