“A modern mathematical theory that radically departs from traditional Euclidean Geometry, fractal geometry describes objects that are self-similar, or scale symmetric...”
Fractals are easiest to see from a middle ground, from a point on a line in time that lets you see the patterns you’ve lived before, and the patterns you find yourself moving into, and how it is the same dance, no matter which part you perform, no matter how you might wish it differently.
I’ve crossed someone, not by my actions, but by what I have failed to do. I have pushed away smothering help – help that is tied to obligation, because I hate the debt it brings. I like to think of myself as self-sufficient, a lone wolf. A pattern standing alone. It is foolishness.
“…This means that when such objects are magnified, their parts are seen to bear an exact resemblance to the whole, the likeness continuing with the parts of the parts and so on to infinity…”
What we see depends so much on where we are standing.
Where is the harm in standing alone, I ask, of carving out my own path? I try to walk away, I listen to the friends and family who say ‘J. is in the wrong, not you.’ I listen well. My anger flares at hard memories that play over and over into the night, her bitter insults. But now J. is facing difficulties that I am in a position to understand better than anyone; however, I've been accused of being selfish, unthankful and uncaring, so I'm afraid to extend any support at the moment…which makes me feel selfish, unthankful and uncaring.
On the other side of the pattern, at the most uncanny time, someone from my past has contacted me. M. is unsure still of how she crossed me, of why I stopped talking to her, unsure of how to seek my forgiveness, but wanting to all the same.
“…Fractals, as these shapes are called, also must be devoid of translational symmetry - that is, the smoothness associated with Euclidean lines, planes, and spheres. Instead a rough, jagged quality is maintained at every scale at which an object can be examined…”
The edges of beauty – of perfection – are rough and chaotic.
It is not easy for me to seek forgiveness from J., because I cannot actually see the wrong I have done. Likewise, I’ve been reluctant to forgive M., because she should know what she’s done, right? Right?
Can’t we all just skip the rough and chaotic phase of forgiveness, and move straight to that place where there is harmony and peace? Of course not.
“…Scientists have begun to investigate the fractal character of a wide range of phenomena. Researchers are interested in doing so for the practical reason that behavior on a fractal shape may differ markedly from that on a Euclidean shape…”
We know what is right, what is wrong. We read it in our most sacred texts. We recite the examples of Buddha, of Jesus. We know it in our hearts. But how well can we live those truths? How well can we match our actions to theirs?
I don't know what to do. Should I call? Should I write J. a note: "Hey. Even though you feel that I'm a terrible person, I just want you to know that I'm thinking about what you are going through. And I do care."
I can take these words, similar to the ones M. has given to me, and pass them on down the line in a seamless continuation of an established pattern. It should be easy, but it's not.
I think the thing that stops me from making any contact is the fear that my words will be treated with contempt.
“…Mathematical physics, for its part, has a particular interest in nonlinear fractals. When dynamical systems--those that change their behavior over time--become chaotic, or totally unpredictable, physicists describe the route they take with such fractals…naming them ‘strange attractors’…”
Over time, water can carve stone. But only over time.
Or maybe I fear the responsibility I’ll be expected to take afterwards; the expectation that I change my behavior, that I bow down and admit that everything I do is wrong, and that I must become more involved, submit to that suffocating connection, all those demands on my time. Our views on family are very different, and they don’t intersect.
“…Most physicists who study chaos (fractals) do so with carefully controlled laboratory setups of turbulent fluid flow. Individual strange attractors have been identified for different kinds of turbulent fluid flow, suggesting the existence of numerous routes to chaos…”
People change only when their comfort level has disintegrated into something they no longer recognize.
M. took a chance, again, that I would treat her words with contempt, as I’ve done in the past. But something’s different now. We’ve both been through rough, life-changing experiences, and without each others’ support. Have we both changed after all these years? Is it possible to maintain that change, should a renewed relationship arise, or would we fall back into old patterns? The same old dance, M. in the lead, and me trying to keep up? Should I say no and turn away, remembering all the old hurts and abuse? Is saying yes tantamount to heating heroin in a silver spoon, at a time when I want a little escape? Will it dissolve into chaos again?
“…The nature of fractals is reflected in the word itself, coined by mathematician Benoit B. Mandelbrot from the Latin verb frangere, "to break," and the related adjective fractus, "irregular and fragmented.”
Yet it forms a solidified pattern spanning from infinitely tiny to beyond the bounds of the universe.
Maybe that’s all we are. Fragmented, broken people, trying to co-exist, to form a pattern that rises out of chaos into beauty.
All text in italics taken from the Grolier Encyclopedia. All fractal art by Victoria B. Brago-Mitchell.