Quasifractal

Quasifractal is a descriptive term used to refer to patterns, signals, or structures that resemble fractals but do not meet the strict mathematical definition of a fractal. The label is often applied when an object shows fractal-like features—such as scaling behavior or self-similarity—only approximately, within a finite range, or in the presence of noise.

A quasifractal typically exhibits approximate self-similarity or scale invariance that holds over a limited interval of magnitudes rather than for all scales. The effective dimension (for example, a box-counting or Hausdorff dimension) may appear non-integer but is not guaranteed to be a mathematically exact fractal dimension. Real-world imperfections, finite resolution, or stochastic perturbations distinguish quasifractals from ideal fractals.

Quasifractal concepts appear in several contexts. In dynamical systems and natural phenomena, observed patterns may look fractal-like despite underlying processes containing randomness or discretization. In computer graphics, quasi-fractal textures are produced with fractal-noise algorithms or hierarchical random fields that mimic fractal detail without implying true mathematical self-similarity. In data analysis and physics, signals or fields can display fractal-like scaling over a finite bandwidth, earning the quasifractal label when strict fractality is not claimed.

Because there is no universally accepted formal definition, quasifractal is primarily a descriptive label rather than a rigorous category. It communicates that a structure shares some fractal properties while acknowledging deviations from ideal fractality.

See also: fractal, self-similarity, fractal dimension, fractal noise.