When your look for structures and patterns, you naturally come across fractals. A fractal is a shape that similarly copies itself but is smaller. You can zoom in on a figure and see similar shapes repeating themselves into infinity. A well-known fractal is the Mandelbrot set named after the visionary mathematician Benoît Mandelbrot who discovered them and introduced the term fractal in 1975. Fractals are everywhere in nature, in the growth of romanesco, sunflowers, nautilus shells, trees, river deltas, lungs, brain cells, waves in the sea, air currents, and fingerprints. And there are many, many more. Could everything growing and developing on earth be based on the same blueprint?
Years ago I read Neil Shubin's book 'The fish within us' a journey through 3.5 billion years of human body history. In this book, he shows the basic design of all limbs. One bone is followed by two bones, some smaller bones, and then even smaller ones of fingers or toes. I think our bones are fractals, they repeat themselves from big to small. The basic design of all limbs can be recognized in a humpback whale's fin, a bat's wing, a penguin 'wing', a pterosaur wing with claws, a lizard's leg, a bird's wing, a seal's leg, the leg of a theropod dinosaur and arm of a human. The limbs of different animals develop based on the same blueprint, so it seems. How intelligent and how simple at the same time! One basic design from which thousands of different species can develop in nature, from flora to fauna?
"Mandelbrot set - Step 11 of a zoom sequence" by Center for Image in Science and Art _ UL is licensed under CC BY-NC-SA 2.0. Created by Wolfgang Beyer with the program Ultra Fractal 3. To view a copy of this license, visit:
Rehearsal of large shapes
The reverse, a shape that repeats itself, larger, does that also happen? I think it should exist. Is the repetition of larger forms beyond our perception? That could be the case if the universe is a grain of sand within a larger whole. Maybe that bigger picture is behind black holes, in which everything disappears. What do we call a shape that repeats and expands? Belgian cosmologist Thomas Hartog explains on Dutch television in the summer of 2023 that the universe expands, the size between stars is growing. Gravitational waves coming from the dark side of the universe are being studied, and are those waves the opposite of fractals? The gravitational waves hold information about black holes collapsing, and researchers think they are likely to hold information about the Big Bang and give more information about how our universe started.
Fibonacci
In nature, processes that develop according to the Fibonacci sequence are a sequence of numbers where each number in this sequence is the sum of the two preceding numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946,... When nature is doing well, it is abundant. In the first year, an apple tree bears one fruit. The second year there are two, the following year 3, then 5 and then 8, etc.
Golden Ratio
The ratio of consecutive numbers in the Fibonacci sequence is the ratio of the Golden Ratio. The Golden Ratio is the ideal, divine proportions, also known as Divina Proportia. You will find them in art, architecture, the proportions of the face, the branches of trees, and river deltas. What we humans experience as beautiful meet the proportions of the Golden Ratio. The effect of looking at nature or art is that we feel good about it. We even feel better and happier. A work of art can evoke feelings of love in us. A walk in the woods or on the beach always makes us feel better. In short, experiencing beauty and nature is good for us.
Patterns play an important role in my work. The process of creating patterns is pleasant and produces a sense of harmony. It gives me positive energy. Without creative therapy, I would never have become aware of this. Making work without judgement, purely for the process, is not always easy for me to apply. There is always a voice in my head telling me things have to be done better or differently. Accepting that it is OK to work in a natural flow and embrace surprises while drawing or painting, is an art in itself.
What happens to our brain while painting, drawing, or engaging in any creative activity causing this positive effect? I'm experiencing a positive impact while working with paint or ink. But what exactly causes this is not clear. Who can help to explore and find answers to these questions?
Benoît Mandelbrot's fractals, the Fibonacci sequence and the Golden Ratio have in common for me that it was the beauty of fractals, the Fibonacci spiral and the balanced proportions that initially caught my attention. But more importantly, they somehow reassure me. Mandelbrot's theory of fractals makes it plausible to me that there is some form of order and organization underlying our universe. No chaos or coincidence. In addition, fractals, the Fibonacci sequence and the Golden Ratio provide guidance and a starting point that I consciously or unconsciously apply in my work.
Mandelbrot's fractals enable us to understand the growth and development of countless natural processes. Would it be possible, with this knowledge, to achieve the most important thing of all, securing a liveable Earth? The answers are bound to be found in nature. Albert Einstein said: 'Look deep into nature, and then you will understand everything better.'
Comments