Tag Archives: Fractal

The Book

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Now available!  The book, Finding Our Way Home: A Spiritual Journey into Earth Community, is being published by my own imprint, Small Bird Press, and available through lulu.com via this link.title-page 

What others are saying:

“Myke Johnson’s beautiful stories from her own journey illuminate the way to reconnecting with ourselves, each other and the entire Earth community. The practices that punctuate the end of each chapter help embody and guide the path of reconnection. A book to savor, it is also a compelling reminder of the legacy of stolen land and genocide, and of the urgency to face the past as a necessary step toward healing and finding our way home.”  Anne Symens-Bucher, Executive Assistant to Joanna Macy and facilitator of the Work That Reconnects

“Myke Johnson’s writings are inspiring, transformative and grounded in the mystic contemplative way of life.  Reading her reflections and meditations gives you a deep sense of connection not only to Mother Earth but to her own personal journey. This is a companion book for all that are seeking a simple but conscious choice of living in peace and harmony on our planet with all of creation.”  Rev. Virginia Marie Rincon, Episcopal priest and Curandera

From the back cover:

In this time of ecological crisis, all that is holy calls us into a more intimate partnership with the diverse and beautiful beings of this earth. In Finding Our Way Home, Myke Johnson reflects on her personal journey into such a partnership and offers a guide for others to begin this path. 

Learning from the Indigenous philosophy that everything is related, she found in her plant and animal neighbors generous teachers for a way back to connection: a chamomile flower, a small bird, a copper beech tree, a garden slug, a forest fern. Their lessons are interwoven with insights from environmental science, fractal geometry, childhood Catholic mysticism, the prophet Elijah, fairy tales, and permaculture design. Each chapter includes practices for further reflection and experience.

This eco-spiritual journey also wrestles with the long history of our society’s destruction of the natural world. Johnson investigates its roots in the original theft of the land from Indigenous peoples and in other violent oppressions between human beings. Exploring the spiritual dimensions of our brokenness, she offers tools to create healing. Here is a map into a new relationship with earth, with each other, and with the Spirit within and between all. Lyrically expressed, Finding Our Way Home is a ceremony to remember our essential unity with all of life. 

You can now order the book for $17.99 (plus shipping) via environmentally-friendly Print-on-Demand at this link:  Finding Our Way Home 

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Photo by Margy Dowzer

Myke Johnson is a Unitarian Universalist minister and earth activist, serving a congregation in Portland, Maine, while practicing and teaching ecological spirituality. She holds a Master of Divinity from Chicago Theological Seminary and a Doctor of Ministry from Episcopal Divinity School.

More recommendations:

“I work with Unitarian Universalist congregational, environmental leaders across the United States. I am keenly aware not only of my need, but what so many seem to experience as a lack, a daily rift between functioning well on Earth, and Living with All Earth in ways that sustain our core. The messages and ceremonies of Finding Our Way Home are as essential, I think, as sleeping. But like sleeping, we try to do without as much as our hearts, bodies and souls need to meet demands in these times. This book is welcome medicine for the beautiful, difficult work and love of our lives.”  Rev. Karen Brammer, UUA Green Sanctuary Program

“As a student of Naiyantaqt, I have, over the long journey of my life, come to appreciate the rhythm of the Great Mystery; the wondrous Consciousness, the empowered understanding and meaning of Manitou, that exists everywhere and in all living and immobile matter. Such connections are profound, relevant, and mark the passage to the future awaiting the enlightened. I am aligned to such kinships and Myke Johnson is a long-time kinship, a seeker of the Divine, a companion in the awe of the Great Mysterious. She boldly embraces the Divine and her quest to connect with the All-Encompassing Mystery. Her book is the re-telling, the sharing of her wondrous spirit, life, and the path to her awareness. Her book will empower true seekers on this Path of Life, a path she confirms by our friendship and mutual journey together.”  gkisedtanamoogk, Maine Wabanaki-State Child Welfare Truth & Reconciliation Commissioner and author of Anoqcou: Ceremony Is Life Itself

“During times of chaos, whether private or public, the human psyche/spirit seeks inner and outer grounding as its home base. Using her own life as a prism of refracted insights, Myke Johnson has created a tool-kit for the rest of us to use in our personal and/or political struggle to survive, and perhaps even thrive. As she shows as well as tells us how to concentrate and tap into our deepest energy and then send it out into the universe in order to affect change, she does exactly that with this book, her own special gift to the world.”  Gail Collins-Ranadive, author of Nature’s Calling, The Grace of Place

“In Finding Our Way Home, Myke Johnson names the many disconnections that modern people constantly experience as the core spiritual issue of our time.  And then through wisely chosen stories from her own experience, she shows us how we might reconnect the inner pieces of ourselves, our relationships in genuine community, and our relationships with the earth into a more integrated whole. She helps us remember our deep belonging with all that is. And that as we engage this process, we are finding our way home.”  Rev. Deborah Cayer, lead minister, Eno River Unitarian Universalist Fellowship, Durham, North Carolina

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Fractals Teach Us That We Matter

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Oak MJ DSC03499There is another reason why fractals matter. Fractals teach us that we matter. By becoming aware of the fractal patterns throughout the natural world, we can see that all things are connected. The circulatory system of the human body branches out like the limbs on a tree. The patterns of waves on the shoreline are similar to the patterns of radio waves beaming through space. Even though we are infinitely small in comparison with the rest of the universe, what happens on a small scale reflects what is happening on a larger scale.

Some of these patterns may seem to be unchanging and eternal, but there is also unpredictability in the system. Scientists use the word chaos to describe this unpredictable behavior. Without chaos, there could be no creativity, because creativity means the emergence of something new and unpredicted.

Perhaps you may have heard of the “butterfly effect.” This phrase was used by Edward Lorenz to describe the impossibility of predicting the weather, despite creating complex computer models that looked at multiple variables. Lorenz found that a small change in the initial conditions would produce large changes when the patterned cycles repeated many times. It was expressed in metaphor as the butterfly effect: a butterfly flapping its wings in South America can change the weather in Maine.

We have creative power as human beings. That means that what we do within our patterns has an effect on the rest of the fractal network. We are part of an interdependent web of all that exists. If we change a pattern in our lives, it reverberates through the rest of the web; it ripples out like a stone thrown into a pond. We have the power to create more beauty, more love, more truth, and more goodness in the web. We never really know what greater effect we will have on the future of the universe. We cannot control the ripples that flow out. But human beings for centuries have observed that acts of kindness multiply into more kindness in the world.

There is a fable told by the ancient Greek storyteller Aesop:

A sleeping lion was awakened one morning by a mouse running over his face. The lion became so angry that he grabbed the little mouse in his paws and was about to eat him up. The terrified mouse begged for his life. “Please let me go,” he cried. “If you do, one day I will repay you for your kindness.” The idea of such an insignificant little creature ever being able to do anything for him amused the lion so much that he laughed out loud and good humouredly let the mouse go.

Then, one day the lion got caught in a snare set by a hunter and was unable to get himself free. The mouse heard and recognized the lion’s angry roars and ran to the spot where he was. He went right to work gnawing at the ropes with his teeth. Soon the lion was set free. “You laughed at me when I promised to repay you. But now you see that even a little mouse can help a lion.” So remember: no act of kindness, however small, is ever wasted.

What we do matters. No matter how small we are, we are intimately connected to the vast universe. We are part of its beauty and its creativity and its love. The patterns in the stars live in the patterns of our hearts. We do not walk alone. These are the lessons I learn from the beautiful geometry brought into the world by Benoit Mandelbrot. May these fractal mysteries teach us ever to be mindful of our power.

What If God Is a Fractal?

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What if God is a fractal? What if God is a pattern that repeats itself from the infinitely large to the infinitely small, a pattern of life and love and creativity?

Human beings have always used images to help us understand the mysterious. Some images of God are like bigger versions of human beings—the Nicene Creed says “I believe in God, the father almighty.” God has often been seen as a father, a king, a ruler, a judge, or a lord.

But when our understanding of the universe grows more complex than these images, some have been tempted to give up on the idea of God. For many people, it doesn’t make any literal sense to imagine a huge king up in the sky somewhere. And if our experience of these authority figures has been difficult, their images are more likely to inspire fear and guilt rather than help us live our lives.

Ferns Full grown DSC05279If I imagine God as a fractal–a self-similar pattern both infinitely large and infinitely small–it helps me to be a whole person—to bring together my reasoning and my heart and my spirit.  It helps my mind to fathom the larger Mystery, as well as to understand the link to that Mystery I feel within my heart.

I am reminded that it is not a new thing to compare God to a geometric shape. The Christian tradition has used the triangle to describe God as trinity. But while the triangle is a static, simple, and smooth figure, a fractal has multiple dimensions, and infinitely complex variations and expressions. That fits my understanding of spirituality—I believe that there are infinite variations in the ways we can experience the holy. As the Sufi poet Rumi has said, “There are hundreds of ways to kneel and kiss the ground.”

There are other metaphors and images of fractal patterns that can expand our idea of God. For example, each cell of the human body contains the DNA pattern that shapes the whole body. If we use our imagination, we might say that human beings are like a single cell in the larger body of the universe and God is like the DNA within each cell, shaping it into its unique being.

Spirituality is a way of connecting our small selves to the mystery and grandeur of the larger whole of which we are a part.  If the larger whole is a fractal pattern, then in some deeply important way, we are already connected by the very pattern itself.

How Can a Mystery as Large as the Universe Connect to a Being Like Me?

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Hubble Image of Spiral Galaxy

Hubble Image of Spiral Galaxy

Another reason that fractals matter, and why I want to explore them, has to do with a very old spiritual quandary. Human beings have long imagined the possibility of an infinite being, a divine being, who is creator and sustainer of the universe, commonly known in our culture as God. Not all human beings resonate with this idea, and the details vary as to what God might be like, but most peoples have some sort of divine being or beings as a part of the stories and values of their culture. I have spoken of God as the larger Mystery of which we are a part.

Many human beings have also imagined that they can have a personal relationship with this divine Mystery. Most cultures have forms of prayer to entreat help from God, and forms of prayer to thank God for help given. Many people also directly experience the presence of the divine in their hearts, the intimate presence of the Mystery.

I know that I have had moments in my life when I felt held in the arms of divine love, that I felt cared for by a Mystery greater than myself. Those feelings are so tangible, that they help me get through my most difficult days. When I feel afraid, I can trust that all will be well, because of that tangible presence of love. When I feel overwhelmed, I can keep on walking forward, held in the memory of that love. But if God is infinite, or if the Mystery is all that is, how can that be? How can a Mystery as large as the universe connect to a being like me, small as a speck of dust?

Fractals have given me a new way to think about this spiritual dilemma. A fractal is a pattern that repeats itself, from an infinitely large scale to an infinitely small scale. What if God is a fractal? What if God is a pattern that repeats itself from the infinitely large to the infinitely small.

Here is how I imagine it. The divine pattern is a pattern of life and love and creativity—it expresses itself in the creative unfolding of the universe. It repeats in the attractions of planets and stars, and in the evolution of life itself. Because fractals continue to repeat in self-similar ways at all scales of size, the same divine pattern emerges at the size of our own human consciousness. We can find that pattern in our hearts, the expression of life and love and creativity. Thus we can find the Mystery in our hearts, as well as in the larger whole.

In this way, fractals offer a solution to the old quandary of an infinite God relating to a tiny human being. By understanding fractals, my intellect can make sense of what my heart experiences of the Mystery. It helps me to make sense of the tender feelings I feel, and to welcome their help for the troubles that life brings. I feel less lonely, when I feel connected to the divine love. It becomes possible to believe that I matter, that I am not just a speck of dust in a vast uncaring universe. I have within me the fractal beauty of the infinite Mystery. Ferns More DSC03600

Fractals In the Forest

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A fractal is a pattern that repeats itself, from an infinitely small scale to an infinitely large scale. We see in the patterns and shapes of nature that there is self-similarity at all levels.

This has both practical and mystical applications. I learned about one practical application from a documentary called Hunting the Hidden Dimension. A group of scientists concerned about global warming was trying to determine how much carbon dioxide was absorbed by trees in the rain forest. They could measure the carbon capture of a single leaf, but how could they count the number of leaves in the forest?

They had an idea. They started by measuring the circumference of all of the branches on a single tree. Because of the fractal nature of the tree, the branches form a regular pattern, dividing at certain intervals into smaller and smaller branches. By measuring every branch, they could determine the ratio between branch sizes. Then they took it one step further. They measured the trunks of all of the trees within a given area.

Imagine it with me if you will. If we walk through a forest we see trees of all sizes—small saplings, huge old giants—there is an endless variety of sizes all around us, seemingly in a random pattern.

Trees MJ DSC03686But it turns out it is not so random. The ratio of tree sizes in an area of forest is approximately the same as the ratio of branch sizes on a single tree. There is a pattern to it. And by learning the patterns, the scientists could compute how many leaves were in the forest, and how much carbon dioxide they would absorb.

Now when I walk through the forest near my home, I remember this experiment, and look with wonder at the trees around me. What seemed chaotic and random before, is now bursting with new meaning, full of patterns that start to reveal themselves to me, as I gaze with deeper insight. My experience of the trees’ beauty expands, and I feel a growing sense of awe.

I find myself looking for fractal patterns everywhere. This new understanding has changed the way I see the world. And it is not only visual. I can feel the patterns in bark with my fingertips, and I start to listen for patterns in the sounds I hear as well. Next time you look at a spider’s web, or gaze into the clouds in the sky, watch for the fractal patterns.

Our ability to measure fractal patterns in the natural world has also given us the ability to create digital worlds that remind us of our own. Fractal formulas are used to generate computer graphics that look realistically like mountain ranges, and rivers, and forests, and clouds. That wasn’t possible just a few decades ago.

Fractals have been used to design antennas in greatly reduced sizes, which enabled the creation of the next generation of cell phones and other electronic communicators. Fractal geometry is enlarging our ability to create new devices that work better, because they follow patterns that resonate with the natural patterns around us.

Why Fractals Matter-Reading the Book of the Universe

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Why should fractal geometry matter to those of us who are not mathematicians? First of all, fractals give human beings a new way to look at the universe. When we can describe something, we can see it better than if we cannot describe it. Because we are better able to see the natural world, fractals enable us to have a deeper relationship to the natural world.

It reminds me of learning to read a book. In order to read, we need to understand the patterns of squiggly lines that form the letters of the alphabet. And then we need to understand how those squiggly lines are combined in multiple ways to form words, and then sentences, and so on. A person who cannot read may look at a book, and it might seem beautiful, or there might be pictures in it to be curious about, but that person cannot understand what it means. When we learn to read the patterns of squiggly lines, the book becomes a doorway into a whole story, and suddenly we have access to a wealth of ideas and thoughts and understandings.

The natural world is like a sacred book; it is the place where we search for truth and beauty and goodness. We might say that the universe itself is our bible. We don’t have to understand the world to appreciate its beauty. Even a baby can laugh with delight at the bright colors of flowers, or try to catch a butterfly. But the more we understand the natural world, the deeper can be our appreciation, and the more its mystery opens up to us. Fractals help us to read the book of the universe.

Fractals give us a way to measure and describe the complex patterns in the natural world. Fractal geometry, in fact, reveals to us the inherent patterning that permeates the universe. A fractal is a pattern that repeats itself, from an infinitely small scale to an infinitely large scale. Complex entities are created from simple designs extended out to many dimensions. We see in the patterns and shapes of nature that there is self-similarity at all levels. Ferns DSC05288

Fractal Spirituality-The Infinite Within Our Souls

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Every
Child
Has known God,
…the God who knows only four words.
And keeps repeating them, saying:
“Come Dance with Me.”
Come
Dance.
                                                     Hafiz

How can a Mystery as large as the Universe find expression within the smallness of our souls? How can we tiny beings experience the Infinite? I found a new way to think about this question when I learned about fractal geometry. Fractals are never ending patterns, with self-similarity at all sizes.

Benoit Mandelbrot was the mathematician who first coined the word fractal, and brought to our attention the possibility of exploring the geometry of the natural world. Fractal comes from the word for broken, and Mandelbrot wanted to explore the rough shapes of nature. Traditional Euclidean geometry could not describe these shapes. Mandelbrot wrote: “Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in straight lines.” Fractal geometry enables scientists to describe the world through complex mathematical formulas.

Mandelbrot Set by Wolfgang Beyer, Wikimedia Commons

Mandelbrot Set by Wolfgang Beyer, Wikimedia Commons

I am not a mathematician, but I was curious to see if I could make sense of the math. Perhaps you have heard of the most famous image associated with fractal geometry, what is called the Mandelbrot Set. It has a dark area that looks a bit like the shape of a bug, with a large round spot, and a small attached round spot. But the edge is what makes it fascinating. It is filled with beautiful complex curlicues that continue to be complex curlicues no matter how much the set is magnified. In fact, it continues through infinite magnification.  (For more images of magnification, see here.)

Mandelbrot Set Magnification by Wolfgang Beyer, Wikimedia Commons

Mandelbrot Set Magnification by Wolfgang Beyer, Wikimedia Commons

But “What is it?” I wondered.

If you have math anxieties, I promise you, I am only going to give a simple explanation with ten sentences. You are also welcome to skip the next paragraph.

A Mandelbrot Set is a diagram of a mathematical equation. The equation is: Z = Z2 + C. You insert a number into the equation, and the equation computes it to a new number. Then you start the equation all over again with the new number. Now here’s the interesting part—we don’t care about the answer. We care about how many times you can repeat the equation, with the number you started with. If you can repeat it only a limited amount of times, that number is part of the Mandelbrot set—and it becomes a black dot on your diagram, part of the black spot. If you could repeat it an infinite amount of times, that number is outside the Mandelbrot set. Depending on how quickly it gets to be infinite, it can be given a different color. Only computers can actually do all of these calculations, but they do them very well, and so we can see the images formed by the equation.

Okay, I’m done with the math part now. (I didn’t go into complex numbers or imaginary numbers, so my apologies to anyone who really knows about all of this. But for the rest of us, it is probably more than enough anyway.) The thing is, when Mandelbrot computed his formula, it created a picture filled with beautiful complex curlicues. And no matter how many times you magnify the picture, you will continue to see similar complex curlicues.

More tomorrow…

 

 

For those who would like more detail about the Mandelbrot Set, see the website Introduction to the Mandelbrot Set: A guide for people with little math experience by David Dewey.