Fractals are intricate geometric shapes that exhibit self-similarity, meaning their patterns repeat at different scales, no matter how much they are magnified. Unlike traditional geometric figures such as circles or squares, which can be described with simple equations, fractals are generated through iterative mathematical processes, producing infinitely complex and detailed structures.
We see fractals all around us, in the branching structure of a tree, in clouds, snowflakes, coastlines, in the system of blood vessels and nerves in our bodies. Fractals can thus be used as a scientific model for many natural phenomena, However, their inherent beauty and intrigue can be a source of artistic inspiration too.
A study in the International Journal of Information and Communication Technology introduces an advanced approach that can be used to create novel images based on fractals. The optimisation algorithm, developed by Junli Wang of the School of Digital Arts at Wuxi Vocational College of Science and Technology in Wuxi, China, and known as the Equilibrium Optimiser (EO), significantly improving efficiency and design diversity.
Fractal geometry was first formalised by Benoît Mandelbrot in the 1970s and has influenced fields ranging from architecture to computer graphics and even music composition. The challenge in fractal art generation has traditionally been the reliance on manual input, requiring expertise and time-consuming adjustments. The new research overcomes some of those limitations through the EO algorithm, which enables a more efficient, diverse, and aesthetically rich exploration of fractal forms, according to the study.
The EO algorithm is an advanced optimisation algorithm based on how natural physical systems balance themselves. Unlike Genetic Algorithms (GA) and Particle Swarm Optimisation (PSO), the EO algorithm adjusts its search strategies dynamically to avoid becoming trapped in local optimisation points, a common problem of many mathematical models. This means that the EO algorithm can fine-tune the parameters needed to generate fractal patterns, producing designs with greater symmetry, complexity, and structural variation than traditional approaches. Wang’s tests show that the EO algorithm works better than older algorithms in terms of the speed with which it converges on a solution and the visual quality and stability it produces.
Beyond its technical contributions, this research raises important questions about the intersection of technology and art. The ability to generate intricate fractal patterns automatically expands the creative possibilities available to artists, designers, and researchers. Unlike hand-drawn or physically painted works, digital fractal art is created through computation, challenging conventional ideas of authorship and artistic intent.
Wang, J. (2025) ‘An alternative method for generating fractal art patterns based on the balanced optimiser algorithm’, Int. J. Information and Communication Technology, Vol. 26, No. 5, pp.54–68.