fractals: pictures of human experience?

what you see below is a fractal. fractals are graphically depicted mathematical functions, maybe similar to how statistical graphs depict mathematics.

fractals are colourful geometrical shapes that illustrate repeated, similar mathematical processes. a very simple example would be the equations 1+2=3, 1+2.2=3.2, 1+2.22=3.22, etc. the equations are very similar (referred to as self-similarity among mathematicians) but with every added step, something slightly new or different is introduced.

thus, fractals, like much of human behaviour and experience, are all about patterns. complex, beautiful fractals are the result of large numbers of repeated, very involved mathematical processes. among others, fractals are used to illustrate and understand living systems that at first glance look chaotic, like weather systems, or the stock market.

or the human experience? i’ve never seen that done before – and would love to try it. i don’t quite know how but a start could be to look at an image like this one and wonder – what could it be illustrating?
blog-fractal-jul-07.png
there are at least two parts to this image. one seems superimposed on the other. the same colours are repeated over and over again: some greens, some reds, some purples and pinks, some blues, and black. what looks like lace or diamonds is actually an almost identical repetition of the much larger structure that looks like it’s flowing from or to the upper left corner. the general mood of the image could be described as dark, passionate, warm and soft.

the richness of this image makes me think that this would definitely be a depiction of the totality of an experience, not only emotions, thoughts or behaviour.

perhaps it is about the love of a parent for a child: the diamond shapes represent all the thoughts, cares and worries about the child – and how out of it a larger, more powerful shape (the child? the parent’s idea of the child?) can grow or be launched. the colours and shapes of these thoughts, cares and worries are manifold and yet there is a clear, homogeneous pattern. the dark shapes could be the shadows that parent and child throw upon each other.

what do you see in this image?

8 thoughts on “fractals: pictures of human experience?

  1. Jan Karlsbjerg

    Interesting take on fractals, Isabella, using a particular depiction of a particular section of a particular fractal function as a Rorschach inkblot test.

    I don’t see any overall shape in the picture, but all the red-to-black transitions look like either sand dunes or stressed colored plastic (some plastics change color along the stress lines when you stretch or bend the plastic).

    BTW, the above fractal does in fact exhibit chaotic behavior: There are sharp borders/edges/zones between some of the rapidly color-changing parts of the image and some of the more slowly color-changing parts of the image.

    A chaotic system is one which while it may have one or more steady states (see disclaimer below), also has “breaking points” where a tiny difference in input value makes a big difference in output.

    For a simple example with two steady states, think about a camel being loaded up with straws. 🙂

    Or better yet (because you can argue that the camel can still walk with tiny fractures in its back): A pencil standing vertically on its eraser rubber bit on a surface: if you push it a tiny little bit, it will wobble; if you put it a tiny bit more, it will wobble more; if you push it a little bit more, it will fall over. Big change in output for small change in input.

    Disclaimer: “steady state” isn’t the right term above, but I’m much sleepy right now.

  2. Renee Rigdon

    I love this line of discussion. So open to individual interpretation. I see the whole of my mood experience. The smooth, flowing stability. The jagged, random highs. And there, off to the upper right, emptiness. It’s smaller than the others, but a part of where my state can be. Beautiful.

  3. isabella mori

    hi jan

    hmmm … never thought of the rohrschach connection. obviously material for another post 🙂

    re the straw that broke the camel’s back – i think that’s referred to as a “cusp catastrophe”: the little thing/event that puts a situation over the top. it’s really cool that you picked up on that (i guess you don’t have a science PhD for nothing) because to me, that’s one of the most interesting aspects of applying chaos theory to psychology.

    in this fractal, the cusp catastrophe is the “decision” of one strand to “grow” out of the lace-like system and start another one of those systems that is so much larger that it looks like it’s quite different.

    it’s not difficult to stay with the example of paternal love here, then, is it? chaos theory is also referred to as the “science of process”. what is that thing/event in the parent/child relationship that’s tipping over, this complex of small ideas/thoughts/behaviours that eventually blows up?

    hmmm … right now it makes me think of the many times a parent tells a child something and nothing happens, nothing happens, nothing happens. often it seems like seeds falling to the ground and drying up. then all of a sudden, years later, the child can pick up on that seed (and don’t these little structures look like seeds, in a way?) and turn it into something big.

    for example, i think of the years of exhorting my older daughter to watch her table manners, seemingly to no avail. suddenly, when my youngest daughter started with the same inelegant behaviours, my older daughter began to admonish HER to mind her manners.

  4. Jan Karlsbjerg

    By the way, “breaking points” in my description above only refers to there being a sudden change, not that something “breaks”. I see that I used two “breaking” examples. :-/

  5. inspirationbit

    hmm… it’s not what i see in that image but what visions it triggers in me: a young socialite in a ruby dress with a pretty lace and lots of expensive looking jewelry, trying hard to appear joyous and happy at a big party, surrounded by a group of admirers, hiding her true feelings – scared, anxious….

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