Having been fascinated by fractal since the late 1980s when I came across them while visiting my great nephew who was studying maths or physics at Munich university I have often found myself being inspired by them, first through psychonautical experience on psilocybin and several years later buying my first fractal generation program, Fractint. Fractals are mathematical constructs and most well known by depictions of their nature as mathematical sets in images. One of the key features fractals is that they are self-similar at different scales. In my early days of fractal explorations I created fractals by zooming in using preset formulae and while turning my screen sideways on an infinite color cycle was playing house music on my computer.
My fascination with fractals today is however deeper then a bleary eyed 'oh wow!' experiences caused by too much of many things. One of the reason humans like fractals is because they resemble nature, and humans (most of whom are psychologically ecophillic) prefer their organic nature. Examples of fractal like forms can be found in snowflakes, ferns and Norwegian fyords. T
Having matured, and studied and become interested in cosmology, transpersonal art and psychology, fractals are incredible tools for contemplation as part of meditative or contemplative practices. Their complexity puts the self into some proportion. I can loose myself in visualizing the fractal mantras and end up feeling at peace, because despite their complexity and chaos they are also still images. Any movement in them is an illusion created by the brain screaming for meaning. Once this tendency is realized we have a choice to cease reaching with our minds for meanings and interpretation, surrender and just be.
Here is a sample of my fractal art work
I have now been producing commercial quality fractals for over a year - sold a few and made a few large canvasses (120cm x 80cm) that are adorning my walls at home. I never get sick of looking at them. I don't get sick of making them either. The act of creation being the meditation and point of transcending.
Some of my recent creations are about experimenting with different color palettes and layering fractals to create composites that are even more in depth and evocative than a single layer fractal.
Fractals are so complex and organic that people have drawn the conclusion that the universe itself is a fractal. Science has however argued that the universe is not fractal in nature as there is insufficient self similarity at all scales as this artical rom space.come reports
https://www.space.com/17234-universe-fractal-large-scale-theory.html
The article however does not seem to acknowledge that fractals as we know them are not self similar at all scales and are self similar within a range of scales and only in certain locations.
One of the best known fractals is the Mandelbrot set, which has a characteristic shape that recurs at all levels of the fractal pattern.
Here is a section of one of the arms from one of the period bulbs (the buds on the main cardoid).
If I zoom in I should get a very similar pattern. If i select another period bulb in the Mandelbrot set a completely different pattern emerges. Thus fractals may produce different types of self similarity in different locations.
If you zoom enough you will find a recurring copy of the Mandelbrot shape (see below), but the self similarity with Mandelbrot recurs at all levels though not necessarily by reproducing the same shape, but one that is similar.
Once you zoom out of a Mandelbrot set (or any fractal actually) you end up with a space where there is no structure (basically empty space).
I am unconvinced by the self-similarity argument made by Morag Scrimgeour and colleagues. Because the universe appears evenly distributed at large scales doesn't mean it cannot be fractal in nature at other scales. A bit like a scatter of many fractal localities that are interconnected in an evenly distributed space. A second argument against jumping to conclusions too soon about the fractal nature of the universe is that we hardly have a complete understanding of the dimensionality of the universe. Some calculations (e.g. string theory) suggest space may be n-dimensional and folded. Our concept of fractals that are visually represented is two or three dimensional at best - four dimensional if we allow for movement in our representation. This may create a misconception of fractals that is derived from the limitations of our ability to image multidimensional fractals. One possibility is that the self similarity of the universe is reflected in the higher folded dimensions which are not observable at large scales. More recently a study has highlighted the multidimensionality in the way the brain processes information which might also suggest a self similarity occurring in the universe in relation to multidimensional organisation occurring in physical and biological systems.
https://www.sciencedaily.com/releases/2017/06/170612094100.htm
Humans may simply not have looked deeply enough and for long enough to study self-similarity in higher dimensions. This does not mean that therefore the universe is a fractal , but it also does not mean such evidence can't be found when we have come to grips with the techniques needed to study the physics of self-similarity in higher dimensions.
Meanwhile, regardless of whether the universe is really a fractal or not, I am having a great time constructing and crafting fractal art to appreciate and share while I am alive and living a life as an intellectual with a sense of aesthetics and spirituality. Hope you enjoy the images. Nyom Nyom Nyom
