How I was inspired to work with fractals

nina

MY INSPIRATION
During a deep meditative state I first saw fractals, although at the time, I had no idea what it was I was seeing! It was my thirtieth birthday, and I had chosen to sit at a cozy and beautiful grassy spot on the ledge of a mountainside in Palm Springs, California. It was my favorite spot to sit and meditate. From a deep state of mind, I saw an image that I can only describe as a tile that was spinning in air. It had suddenly appeared from the corner of my right eye and looked like a piece of bread being thrown into the air as it went into a spin

It had suddenly appeared from the corner of my right eye and looked like a piece of bread being thrown into the air as it went into a spin before me. As it was spinning, I could see its colors. The colors appeared as big blobs of red and blue. The tile finally came to a stop far out into the distance. I was attracted to it but honestly it had no special significance to me. Then, out of nowhere, from the corner of my left eye at the edge of my peripheral vision, another tile began spinning wildly. It spun over to the first tile and locked neatly on to it as it came to a stop; the two had a smooth landing. The tile was also colorful but was quite different from the first. This too meant nothing to me. Then, a third tile moved into sight spinning from the right side and locking into the first two. And, then a fourth tile came from the left, followed by a fifth from the right. I could see that each one was different in color. They stacked themselves neatly one on top of the other. Once they did this a magnificent design appeared. I got to see the most beautiful kaleidoscopic image. I stared at it for quite some time. I somehow disengaged the tiles from each other in order to inspect them individually. Then I put them back together again to appreciate their collective design. Separately they meant little or nothing, but together they seemed to mean something very important. After further gazing, in the center of the image an opening appeared and I heard a voice say, “This is the key to the universe. All you need to do is figure out how to stack the tiles and they will form a vortex for you to pass through. It will take you where you need to go and will provide a key to the universe; your universe, the universe as you will come to understand the meaning/mystery/the message.” It had suddenly appeared from the corner of my right eye and looked like a piece of bread being thrown into the air as it went into a spin before me. As it was spinning, I could see its colors. The colors appeared as big blobs of red and blue. The tile finally came to a stop far out into the distance. I was attracted to it but honestly it had no special significance to me. Then, out of nowhere, from the corner of my left eye at the edge of my peripheral vision, another tile began spinning wildly. It spun over to the first tile and locked neatly on to it as it came to a stop; the two had a smooth landing. The tile was also colorful but was quite different from the first. This too meant nothing to me. Then, a third tile moved into sight spinning from the right side and locking into the first two. And, then a fourth tile came from the left, followed by a fifth from the right. I could see that each one was different in color. They stacked themselves neatly one on top of the other. Once they did this a magnificent design appeared. I got to see the most beautiful kaleidoscopic image. I stared at it for quite some time. I somehow disengaged the tiles from each other in order to inspect them individually. Then I put them back together again to appreciate their collective design. Separately they meant little or nothing, but together they seemed to mean something very important. After further gazing, in the center of the image an opening appeared and I heard a voice say, “This is the key to the universe. All you need to do is figure out how to stack the tiles and they will form a vortex for you to pass through. It will take you where you need to go and will provide a key to the universe; your universe, the universe as you will come to understand the meaning/mystery/the message.”

It had suddenly appeared from the corner of my right eye and looked like a piece of bread being thrown into the air as it went into a spin before me. As it was spinning, I could see its colors. The colors appeared as big blobs of red and blue. The tile finally came to a stop far out into the distance. I was attracted to it but honestly it had no special significance to me. Then, out of nowhere, from the corner of my left eye at the edge of my peripheral vision, another tile began spinning wildly. It spun over to the first tile and locked neatly on to it as it came to a stop; the two had a smooth landing. The tile was also colorful but was quite different from the first. This too meant nothing to me. Then, a third tile moved into sight spinning from the right side and locking into the first two. And, then a fourth tile came from the left, followed by a fifth from the right. I could see that each one was different in color. They stacked themselves neatly one on top of the other. Once they did this a magnificent design appeared. I got to see the most beautiful kaleidoscopic image. I stared at it for quite some time. I somehow disengaged the tiles from each other in order to inspect them individually. Then I put them back together again to appreciate their collective design. Separately they meant little or nothing, but together they seemed to mean something very important. After further gazing, in the center of the image an opening appeared and I heard a voice say, “This is the key to the universe. All you need to do is figure out how to stack the tiles and they will form a vortex for you to pass through. It will take you where you need to go and will provide a key to the universe; your universe, the universe as you will come to understand the meaning/mystery/the message.”

For years I carried that memory with me of that day and I hoped that one day I would understand its meaning. Eighteen years later, during an Integrated Energy Therapy (IET) Course, the vision suddenly came back to me with new insight.
Although I started to make fractal art before taking the IET course, it wasn’t until that moment when I put it all together. It happened in a brief discussion at the end of the class with my teacher that a door to the mystery opened. I was showing her some of the fractals in printed form and began to explain how I made them. We discussed their value and the usage of the fractals when she asked me what had inspired me to create these beautiful images. She added her observations by saying, “To me, they are like keys, insignias, stamps or seals.” That’s when it happened as she was referring to the patterns as “keys” that it triggered the memory of the long-ago mediation experience, eighteen years before.

HISTORY OF FRACTALS – DR.MANDELBROT
Fractals were first seen in the 1980s with the development of computers and the silicon chip. Although long before that in 1917, a French mathematician, Gaston Julia published several papers having to do with complex numbers which later were called “Julia Sets.” He drew the formulas by hand, guessing at what they might look like. With the discovery of the silicon chip, Dr. Mandelbrot (1980) and his team began by inputting the Julia Sets and saw patterns appear. They were amazed at the extraordinary patterns, and were taken aback because they looked very similar to what Julia had drawn in 1917. To study further, Dr. Mandelbrot took the simplest of the Julia Set formulas and inputted that into the computer. At first, the design looked like a big blotch which they called a “bug.” But as it became more precisely drawn, they saw stuff around it that they called “junk.” They took a closer look at the “junk” using magnification and some of it fell away, but other parts of it actually continued on and some patterns began to repeat. After greater magnification they saw the original design of the Julia set did indeed repeat itself. At that point Mandelbrot knew he was on to something big and he coined what he discovered as the “Mandelbrot Set.”

The simple Mandelbrot formula uses numbers and iterations. One of the numbers in the formula will increase, while the other will descend to zero. The number zero represents the black we see in the Mandelbrot Set, the absence of light. The exponential number and its pattern that goes on forever will randomize the colors that we ultimately can see. From what they saw Mandelbrot and his team were able to interpret how quickly the pattern moved out to space, towards infinity. Basically as you magnify the formula, it goes on forever and you will continue to see new generations of “baby Mandelbrots.” The images look like islands in a sea of chaos. And, as the formula is magnified again and again it splits and continues in random directions. This type of bifurcation is typical of a class of mathematical entities called fractals. The Mandelbrot set is the most famous. Hence, fractals simply mean highly detailed patterns at varying degrees of magnification, and they are endless—both literally and figuratively. Fractals are more simply described as geometric shapes that have detail on all scales of magnification; details no matter how big or how small you make them. Dr. Mandelbrot called them “fractal” because it conveyed a sense of being fragmented, fractional, and irregular.

Sometime later, Dr. Mandelbrot and his team took their studies to nature attempting to observe irregular shapes. After all, a tree isn’t merely a triangle or a square, and neither are clouds just varying sizes of circles. Yet, both have a continuous pattern changing slightly as their patterns repeat. There is an example and an extension of classical Euclidian geometry known as Fractal Geometry. And, as humans, we are familiar with these shapes in our subconscious minds as well as in our organized and conscious daily lives. Looking at the fractals makes you feel you are looking at a map from a far distance. The map will not make much sense until you get closer to the details.

Comparing the two– the Mandelbrot set and Nature, it shows they both begin with a simple formula that becomes very complex. Like all living creatures, they are biologically known to start simply, and then become extremely complicated, emanating from simple laws of physics and chemistry. And yet, like the leaves of a tree, each small piece looks very similar to the tree as a whole. Therefore, the replications of the patterns in nature are believed to NOT be random.

Many people are familiar with the Fibonacci sequence of numbers, 1,1,2,3,5,8, 13,21,33, 54. The numerical sequence represents the way all sunflowers grow. Pine cones and the shape of the nautilus are also in spirals. Humans are comprised of fractals and it has been wisely said that, “Man is the measure of all things.” The arm span measures the exact length of a human being’s height supporting the belief that there is a formula at work. There are many comparisons that can be made. For instance, the wiring of the human circuitry of the brain replicates the star systems of our galaxy, and, the branches of human lungs do look like trees. These patterns repeat themselves throughout nature, in and outside of the human body. Once you begin to develop a fractal geometer’s eye, you will begin to see fractals everywhere!

With relationship to ancient art, long before we had computers to visualize and create patterns, people saw fractals and used them in creations and in design—in stained glass windows, in the patterns of rugs, in textile designs, tiles and in mosaics, just to name a few. We can recognize these patterns most particularly in Islamic art. These examples lead us to ask the question “Is there a connection between the brain and fractal geometry?” We do know there are cells of the brain that handle shapes and boundaries and there are cells that handle color. Perhaps, the brain has cells that handle fractal computation? However, that is something we do not know yet.

In 1928 a patient of Carl Jung’s drew designs representative of fractals. As you may know, Jung believed in the collective unconscious; “the idea that there is a deep well of consciousness compounded from primordial universal images we [cannot BUT] share, which is known to be the substructure or background of awareness.” And he noted that when we draw Mandalas from the center outward, humans tend to process their personal issues or challenges and use them to gain greater clarity and increased energy which we choose to apply to our lives. Through viewing, we are similarly informed simply by gazing at these designs. Mandalas become vehicles for individuals to connect with our Buddha nature. They transport our mundane consciousness to realms of enlightened awareness. During these states of expanded consciousness, we open ourselves fully to being connected to all possibilities.

he mind clearly finds resonance in the Mandelbrot set. But there are other wider implications to this particular mathematics. That is, it may offer new insights into how the universe works. Specifically, we begin to ponder how much in life is pre-determined and how much of life happens randomly (or- is due to chance).

In relationship to sacred geometry, it is believed that energy lives in sacred forms and shapes. Pythagoras taught sacred geometry as an ancient language. Geometric formations contain information and communicate ideas not just on a cognitive level, but often at a deep cellular level. They inform us cellularly, just as our cells, the building blocks of our physiology inform our bodies, providing a template for our development. Our cells are vehicles of involution; the movement from spirit to matter, as well as vehicles of evolution; movement from matter to spirit.

Some say that the Mandelbrot Set is the thumb print of God. Others believe, like Jung, that these mathematical patterns are linked to our collective consciousness. What all agree is that fractals surround us. These shapes hold information on a minute level. People who have one or more of my fractal art tell me they feel positive energy and clarity coming through them. They speak of the helpfulness of their fractal during meditation. Some have found deeper meaning to dilemmas for which they have been searching for a long time. Yes, they are great for the sheer beauty of admiring them because each one is unique and they cannot be easily replicated without the Julia seed formula. But for many, the fractals serve a higher purpose, not on a cognitive level, but on a deeper subconscious level. I am pleased to say that everyone gets something different from them. Each person resonates with a different one of my fractals depending on where the person connects with the movement that is part of the patterning. They are deeply personal. Take a look and see which you are drawn to. Mostly, I invite you to enjoy (or NJOY) them. I believe, like Jung, I am bringing them forth from the depths of the endless fountain of our collective unconscious.

 

 

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