Feature Story

Fractals in Nature: Self Similarity and Karma

The simplicity of repetition
Production Model
It is the big picture...
...that you can view in details
You will find meaning in mirrors..
...and this is contained in the heart
I gain strength through your perseverance
She waits for our understanding

It wasn't until the last quarter of the 20th century that the scientific establishment began to understand the meaning of nature's fractal forms. This understanding is owed in part to Benoit Mandelbrot's solution to some age old mathematical monsters that defied the traditional geometric conventions. While I myself do not attempt understand the feedback loop equations that bring us the iconic fractal plots, the beauty of its understanding is not lost. Beauty in itself is not the only point of this exercise fortunately. I would like to plot a path to the harmony between our mind; its patterns and how nature can help us understand the relationship of a part to its whole.

Prototype and Production

What if nature was one unified mind made up of its myriad of individual parts, which together constitute the whole of consciousness? As parts, we identify with our own separate consciousness as the singular source of understanding in our lives. This separateness is simply the side effect of being apart. In the picture Prototype, the ice does not know its similar heritage to the leaf, Production Model. While we may see the visual similarities, the ego reels at the concept of nature emulating itself in two seemingly dissimilar forms of mater.

Understanding the fractal Nature

A pillar of fractal theory is the concept of Self Similarity. The concept of natural (and manmade!) forms being all fractal at all levels is quickly sinking into many fields of scientific inquiry. The repetition of patterns, expressed in the generated plots of feedback loop equations is the key to understanding Nature. As we see in this set of pictures, tips of tree branches are self similar in its repeated patterns. Notice the same in the tree as a whole in its companion photograph. Furthermore, we can clearly recognize the similarity between the two very different trees when viewed side by side. Surely by design! Surely Nature has arrived here after millennia of trial and error by reason. Only the fittest survive. A Miracle?

We view the whole, by examining the details

While this concept is seemingly paradoxical, Nature provides a visual touchstone with which the ego can affix itself for unfolding. Life itself is fractal; Thoughts are fractal in structure, theme, and concept. How many times in your life have you seen repeated themes in seemingly disparate situations? Do you glance at the clock only to find it reads a particular time more often than others? We arrive at many day to day solutions to problems by drawing on knowledge of the past, or other problems. Karma also can be conceptualized from afar through the lens of fractal theory. Repeated patterns, thoughts, actions, themes in our life, these are but one phase of karma. Fractal repetition from the unattended thought, to the wide overview of one's life can be understood by examining any part of the whole. I will not dwell here; I will leave you the reader, the part, to unfold our unified mystery. View the mountain and its blanket of trees, the rock and its accompanying shrubs.

A shadow's mystery revealed in our veins

There are a number known ways to enlightenment of the mind. I spent some time with a shaman who espoused the concept of "Every action, every thought, every feeling a prayer." Using our fractal code and what we learned about thoughts previously, we might see how we can unlock these patterns through examination. We will use the working definition of prayer here to be: Examination through meditation, which gives rise the deep feeling of love that can only be felt when we accept we are but a part of the whole. Our true heart is given freedom as we rejoin the whole through this symbiotic relationship.

Fear and shame are the fractal shadow pattern outline of meaning and joy.

The innate human need for unity, community, kindred spirit has given rise to the concept of religion. This need is fulfilled when the ego realizes that by examining itself, accepting itself for the beautiful part of a whole it is. All thoughts are part of a whole, larger picture, linked by its neighbors. Indeed we are not parts, but connected to a whole, whose image is mirrored in our own thought-shape.

How can I understand this better?

New thoughts and concepts are always hard to fully grasp for all of us. The fractal nature of thought dictates that we must see continued repetition for the mind to understand the genetic helix of a concept. Nature has been at this for a while; you will never be able to grasp it all. . I'm sure some of what I talked about seemed obtuse to say the least. If in fact, you are intrigued by some of the concepts I talk about in this article, I encourage you to do a little research on fractal concepts and current theory. There is some really exciting work going on, for example did you know: In a forest the distribution of the sizes of individual trees exactly matches the plot slope of individual branches in a single tree?

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21 responses

  • Ramon Terrado

    Ramon Terrado (Deleted) said (23 Dec 2008):

    Great work explaining fractals. And as an image is worth a thousand words, photos showing examples of fractal structure in nature. Well done!

  • Cory Verellen

    Cory Verellen said (23 Dec 2008):

    Thanks! I tried to find examples that push our limits of fractal understanding. Finding self similarity in two things normally not associated to illustrate that nature is one mind.

  • Renee Cettie

    Renee Cettie said (29 Dec 2008):

    Enjoyed reading your essay. Recently saw a program on fractal concepts and the thoery. All very interesting and excellent photo examples.

  • Misha M. Johnson

    Misha M. Johnson gave props (29 Dec 2008):

    I very much enjoyed your article. Thank you for taking the time to lay our the theory. I've heard much about this and have always wanted to know more. You've reinvigorated my interest. I will now meditate on this much more deeply.

  • Kayla Vandeburg

    Kayla Vandeburg gave props (29 Dec 2008):

    i love this!!! you have my vote

  • Niki Conolly

    Niki Conolly gave props (30 Dec 2008):

    haven't read the whole of it yet, but will do for sure. And not sure I agree with everything, but I do like your shots.

  • Laurie Taylor

    Laurie Taylor said (17 Jan 2009):

    This article was mind BOGGLING! It seemed that the most important words in the philosophical world of nature were put in a hat and then pulled out one by one to make this article. I still dont know what the point was and I read it twice. While I appreciate the importance of understanding the nature of fractals - I dont think 99% who read this would completely understand the simple nature of it all? "Karma also can be conceptualized from afar through the lens of fractal theory." CREEPY!! "Repeated patterns, thoughts, actions, themes in our life" SIMPLE AND WE CAN UNDERSTAND THIS : )

  • Chelsea W

    Chelsea W gave props (22 Jan 2009):

    Love it :)

  • Mary Witt

    Mary Witt said (26 Jan 2009):

    I have read books by Eckhart Tolle. He doesn't mention fractals, but he dors say that we are all part of a whole. He states that our thoughts keep us apart. We are so much more than what we THINK. I believe this, but I have a hard time thiinking positively. I am going to check out this fractal theory and maybe it can get me OUT OF MYSELF and INTO THE WHOLE. Thanks. I needed to read that.

  • Cory Verellen

    Cory Verellen said (26 Jan 2009):

    mary, this fractal 'theroy' is just homegrown art on my part. Not to say though its any less true, just linking karmic teachings and nature's fractals is novel. im not surprised that mr. tolle does not market this idea. i really need to re-write some of this article for new ideas and clarity. im glad so many people have enjoyed my musings!

  • Stefan Schafer

    Stefan Schafer said (27 Jan 2009):

    Hi Cory, thank you so much for your inspiring essay and photographs!
    I do believe, no I know, everything I am and do is interconnected with everything and everyone I meet and vice versa. Years ago here in California, I saw a bumper sticker, "practice random acts of kindness" it said. I didn't know what it meant. But I tried it and it became a habit. I felt strange at first, but it felt good. And then I noticed other people seemingly doing the same thing at random (with me or other people). Made me feel good.
    I also believe in hearing-out a friend or not so friend goes a long way to understand why/how they're acting a certain way. I learn a lot about myself this way, too.
    BTW, I saw s/th a while back on tv about forests and how the leaf structures correlate to the overall growth of the forest. Awesome to say the least. I think it's a profound finding.
    Your essay reminded me of all that. I thank you again, Stefan

  • Cory Verellen

    Cory Verellen said (28 Jan 2009):

    Stefan, That tv program you saw on fractals and forests; I saw the same, just as I was solidifying all this in my head. trying to come up with a physical analogy it came just as I was thinking on it. I suppose it could have been anything about interconnectedness, but alas it is nature and fractals.

  • cynthia austin

    cynthia austin said (31 Jan 2009):

    I concur with the idea that all of nature is fractals. Back in massage school our Anatomy and Physiology instructor showed us the repeating patterns of bodily construction: how the connection of humerus, radius and ulna are repeated in the leg with femur, fibula and tibia, how our metacarpals and metatarsals mimic each other. How there are six main joint types that repeat throughout the body. The patterns extend themselves inward to bone and muscle shapes and attachments. The pattern fractalizes further the smaller the focus: organs and organelles, things that fit within other things and are replicas of them (babies in mothers), things that change in predictable ways over time (birth, growth, maturity, decline, death happening to each person and each generation). Patterns that are composed of fractals that are all around and fit into each other like Russian dolls.
    The only reason why we still have this debate with so much evidence that proves that all is one same thing is that we are like fish in water, oblivious to our own fishness, our own way of being because we have nothing, no non-fishness, to which it can be compared to be considered real itself. In other words, we just can't see the obvious, that what we're looking at and looking for is also ourselves.

  • cynthia austin

    cynthia austin said (31 Jan 2009):

    Oh yeah. I can add this much more from what I believe I'm close to figuring out about it all: If everything is fractals and there is such a thing as energy, then everything is energy. Here's why it is said that energy is neither created nor destroyed: because it is a fractal! Therefore, we are very literally energy fractals...eternal. The thing most people don't want to examine is the next logical step. If we are energy fractals and we discover that fractals are all there is, then we must come to the conclusion that we are...God.
    That reminds me of a friend's mushroom trip in which he saw the whole world as fractals, but that's another/the same story.

  • Cory Verellen

    Cory Verellen said (31 Jan 2009):

    I love your enthusiasm Cynthia. I wish everyone had that joy of discovery. Maybe you should write us a story about your theory.

  • Rahul Dev

    Rahul Dev said (6 Mar 2009):

    I'm a highschool student at the moment and I feel very proud that my school offers a course in Chaos Theory and Fractal Geometry. That's right; contrary to popular thought, chaotic systems beget fractal patterns. Mathematically dynamic functions (feedback, usually) often seem too complex to analyze through conventional end-behavior means but take on new light when peered upon geometrically. I encourage the author and others of you interested in this field to read our class's adopted textbook "Does God Play Dice?" by Ian Stewart. (Don't worry; this book isn't religious, the quote comes from the quantum theory skeptic, Albert Einstein. Chaotic systems also give rise to probability models such as those used in quantum theory.) Additionally, those of you interested in fractal patterns in nature photography should check out Benoît Mandelbrot's first book, "The Fractal Geometry of Nature."

  • michael borders

    michael borders gave props (21 Jun 2009):

    Beautiful images!

  • Suzanne Smith

    Suzanne Smith (Deleted) said (22 Aug 2009):

    Very inspiring. Thanks for getting me interested in this site. I just watched the NOVA show on fractals and had some of the same thoughts you put in this article. I am doing studies of waves lately and Im sure there is a reason we feel a burst of energy at the beach. This is all leading somewhere but Im not sure where.

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