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Marianne Goudswaard

A crumpled ball of paper or the fractal dimension

Updated: Jan 28, 2023


One day I received a package wrapped in silk tissue paper. The fragile paper did not reveal the gift yet. This increased my curiosity. The silk tissue wrinkled and created a pattern in the paper. Similar patterns can be seen in leaves or when the earth's crust has become dry, They emerge in ageing skin or can be seen in broken glass. The effect is also called 'craquelé' in ceramics.


Can you draw on the crumpled silk tissue paper? The paper is so thin that the marker goes right through it. Would it be better with a brush and Chinese ink? The ink finds its way drop by drop over the irregular surface of the paper. Sometimes the ink accumulates and then flows freely. A few hours pass unnoticed with the interplay of the thin paper and the black ink. Gradually, a pattern of black lines emerges on the paper. In a way, the pattern looks familiar. It reminds me of structures photographed on the beach. But also of the medical drawings by Ramón y Cajal, a Spanish neuroscientist from the 19th century. He made beautiful drawings of our nervous system and our brains that are still used today in textbooks all over the world.


An unpredictable canvas

My eyes are drawn to graphic patterns over and over again. On the beach, in the forest, the local trees, traces of paint on the road, cracks in the asphalt, peeling paint on walls, patterns in flowers and plants. Everywhere, you can come across fascinating patterns which are beautiful, and occur in so many different places.


Searching for information about patterns and structures on the internet, I had already come across the name of mathematician Benoît Mandelbrot*. This time it is a guide** on what a fractal is and in which fields fractals are used (loads!). The following quote gives me goosebumps. "A great way to explain dimensionality is thinking of it as a measure of roughness, or how well a given shape fills the surrounding space. A sphere for example fills 3 dimensions of space because it is a solid object. A piece of paper fills 2 dimensions of space. A fractal can be somewhere in the middle. Imagine you take a 2-dimensional piece of paper and crumple it up into a ball. That ball of paper now has a length, a width, and a depth, but it is also wrinkled and has lots of voids between the crumpled layers of paper. Because the crumpled paper ball is not completely solid, it has a fractional dimension value, likely somewhere around 2.5 (between the 2-dimensional flat piece of paper and the 3-dimensional solid sphere)." end of quote.


The patterns I create and find in lots of different places are called fractals. To learn that a crumpled piece of paper exists in the fractal dimension and I always crumple my paper for my work is another remarkable thing. To make work in combination with the knowledge found on the World Wide Web becomes a journey full of discovery that becomes part of my art.


Only now do I understand that scientific research has many similarities with a creative process that is part of the creation of art. A complicated calculation, mathematical formula or scientific theory is of the same beauty as art. Science can touch you and give you new experiences and insights like art does.


* Benoît Mandelbrot was the first in the world to understand and interpret these patterns and to find the mathematical formula that underlies what he saw as rough shapes that he called fractals. The word fractal is derived from the Latin word “frāctus”, which means "fractional" and "broken". Nothing in nature around us is an exact square, round or conical shape, Benoît Mandelbrot argued. All natural forms have rough, ragged edges. They develop and copy from large to small to infinity. The repetitive shapes are not exact copies, they resemble each other, but have their own shape that makes them unique. Benoît Mandelbrot discovered fractals in the natural development and growth processes, but also in many other fields, such as economics.








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