Often, art creation or design not intentional use mathematic concept which understandable few centuries later. Arts and mathematic growth based on limitation and creativities of thinking.
Mathematic concept must logic, while arts do not always logic. Arts can growth wild, break logic border. So, it is not weird if mathematic need long time to understand arts in it concept. For example is Islam Decorative Arts. This arts obvious use decagonal quasicrystal geometry, and figured at 1970ers sucah as in Escher.
Fractal and Chaos Theory
Fractal popularized by Benoit Mandelbrot. Fractal is mathematical concept which study pattern sameness at generated scale. Simply, fractal appearing signed that there is pattern repetition or self-similarity in different scale of object.
Simple example is Sierpinski Triangle. In this triangle, every triangle has pattern repetition with others inside. Fir leaves are perfect example of fractal appearing in nature.
Computer technology gave big contribution of fractal birth. Calculation of pattern repetition in different scale in exact. Fractal in different scale is so important because fractal is sign of ordered thing in chaos system.
Before chaos theory founded, chaos condition equalized with random/disordered condition, without rules, without structure, and impossible to made mathematical models. But after chaos theory founded, we knew that complex system, un-lininer, and very sensitive at beginning condition, there is order in disorder, that is fractal.
Fractal geometry differs than Euclidean geometry. Euclidean geometry only able to classified objects in to integer. For example, cubic is 3 dimension things, square is in 2 dimension, and lines in 1 dimension. Fractal geometry receive objects in decimal dimension, such as 1,5 or 2,75.
Fractal in arts design? Every time you see traditional motif, like batik, you’ll see a fractal. Batik is traditional cloth from Indonesia, with incredible motif/pattern and full of philosophy. From 20o sample of batik pattern, it show that batik has 1,5 dimension of fractal.
Fractal appearance in batik determine by its decorative technique, called as “isen”. Isen is technique that fulfill big pattern with certain small pattern. Isen in symbolic meaning is effort to make perfection and give meaning to overall object.
Batik created as interaction between human and environment (look at The Everyday Concept of Architecture), and other art culture object. Human understanding nature and translate it with painting in technique. Interaction between human and nature is un-linier interaction, involved related factor, like technology, culture, mysticism, economy, and geography.
So fractal in many design or arts object is social complexity form, continuous interaction, seems disordered, but truly arranged.