The multifractal fields above were generated using the Fractionally Integrated Flux (FIF) model as described here, a mathematical method proposed in 1987 by Daniel Schertzer and Shaun Lovejoy for simulating scale invariant random fields.

A remarkably wide range of possible scale invariant fields can be described with just three parameters:

• H: Controls "smoothness" — how strong larger-scale fluctuations are vs. smaller ones.
• α: Controls extreme events — lower values create occasional giant spikes.
• C₁: Controls clustering — when large, activity concentrates in small regions.

All fields generated using the Python package scaleinvariance.