Fractals and More
God has been teaching me about fractals, His incredibly intelligent design, His complexity and order, His plan and love for me….I want to “Shar-on” with you!
Don’t you love it when God reveals truth to you? You learn something new-at least new to you- about creation or the very essence of life, something about our existence in this world that you had not considered before? Something that goes so far beyond the human intellect that it boggles your mind? As you dig deeper, bit by bit the picture unfolds, bit by bit things begin to make more sense. A blurred picture comes more clearly into focus. A new discovery excites you and gives you a fresh new perspective. The urge to keep learning and searching for answers keeps you up at night, but confirms hope in your spirit that there is so much more than we know, that there is a much greater plan than we realize. Recently the Lord has been showing me a bit more about His incredible intelligent design and about His purposes. He has done this through learning about the world around me, through the reading of His word, through my life experience and through the people He has placed in my life. It is not that there is something NEW, it is just that I am DISCOVERING it; it is new to me! When we search, God gives us a new understanding of something not so new to Him! It is as if God has set Himself in “discoverable” mode. My husband knows that technology is not my forte, but I do know that if I want a device to connect to my phone by Bluetooth, I have to make my phone “Discoverable”. Then the device searching will be able to find my phone and make the connection. If we are “searching” for a connection and if it truly exists, we will be able to find it. Our society is all about connecting. We have e-mail, Facebook, Linked in, Twitter, Snap Chat, Instagram, the list goes on. But the idea of connecting is not new! Since the beginning of time, God has wanted to connect with us. He WANTS us to find Him in order to communicate with Him and have an intimate relationship with Him. He loves us so much that He has made Himself “Discoverable”. One of the ways He has done this is through His creation, His incredibly intelligent design! Romans 1:20 says, “From the creation of the world, God’s invisible qualities, His eternal power and divine nature, have been clearly observed in what He made. As a result, people have no excuse.” As we examine His creation, we learn more and more about the character of the Creator. The invisible becomes visible. He is not new, He has existed from eternity past to eternity future. His word says, Jesus Christ is the same yesterday, today and forever. Ecclesiastes 1:9 says, “There is nothing new under the sun.” As we search, we discover; bit by bit the unveiling begins. Jeremiah 29:13 tells us, “When you look for me, you will find me.” This excites me….and exhausts me, as I realize how little I know and how much more is yet to be discovered. The amazing thing is that God has not just made Himself “discoverable”, but, because of His great love for us, He is also actively “SEARCHING” for us! In Ezekiel 34:11, “God says, I will seek and find my lost sheep.” Are we open to make ourselves “discoverable” and are we willing to accept the connection?
I love it when God makes us stop and take notice of His divine nature! In my Pre-K and Kindergarten classes we have been learning about Spring. We have been pleasantly surprised by how new life springs from what would appear to be dead. We watched as a “resurrection plant” came to life within minutes when placed in water, and as a “Glad” bulb, appearing dead, after being placed in the right environment (rich soil, water, sun and TLC), sprouted and literally grew right before our eyes. We learned about the delicate, yet “tough as nails” snow drop plant which has the strength to push its way up through the frozen ground. We are learning about the wood frog whose heart stops beating when it hibernates and 65% of its body freezes, then, when warmer weather returns it thaws and is as good as new! An incredible design! We saw robins, caterpillars, butterflies and two bunnies almost right on our back porch! All this reminds me of how even through the dark cold winter of our lives, because of God’s design and grace, we too can experience a sprout of new life in Him! How refreshing!
In the midst of welcoming in Spring and the new life it has to offer, I have been reflecting on “fractals”! You are probably asking what in the world a “fractal” is. Up until just recently, I had no idea either! My only knowledge of the word, was from our daughter Amanda who drew it to my attention.
A few years ago, our entire family read a book called “The Shack”, by William P. Young. This story had a profound effect on each of us, in particular Amanda. “The Shack” is a fictional story about a father (Mack) who through a tragic event in his life enters into a “great sadness”. Years after the event, God invites him to “the shack”-the very center of his pain- where he has an encounter with God: God the Father, (Papa), Jesus His Son, and the Holy Spirit (Sarayu). Many things resonated with Amanda’s spirit in this book and it sparked a deeper love and a better understanding of God. It also inspired her to do a painting expressing some of the images that impacted her as she read.
I remember Amanda speaking in particular of “fractals” which are referred to in “The Shack”. While at “the shack”, Mack is invited into the garden, which turned out to be much more “chaotic” than the orderly garden he had imagined it would be. Sarayu said that “From above it’s a fractal…something considered simple and orderly that is actually composed of repeated patterns no matter how magnified. A fractal is almost infinitely complex. I love fractals so I put them everywhere.” Mack replied, “Looks like a mess to me!” Sarayu goes on to explain that this garden is Mack’s soul; that this mess is really him. “Together you and I have been working with a purpose in your heart. And it is wild and beautiful and perfectly in progress. To you it seems like a mess, but to me, I see a perfect pattern emerging and growing and alive-a living fractal.” Later Papa explains “My purposes are always and only an expression of love. I purpose to work life out of death, to bring freedom out of brokenness and turn darkness in to light. What you see as chaos, I see as a fractal.” I have been thinking about this as it applies to our own lives. Sometimes, we cannot make sense of our brokenness, our chaos and our messes, but when we get God’s perspective, this sheds new light. We ALL have brokenness in our lives in some form or another. Although we do not understand all the purposes for the circumstances we face, it is refreshing when a glimmer of light pierces our darkness, offering a taste of hope; just enough light to take the next step, enough hope to give us the courage to press on. What it requires is faith, just a tiny amount, as small as a mustard seed! When we put our faith in Him, He begins to reveal that even our brokenness can be seen as a fractal from God’s perspective; something orderly, complex and beautiful! In the midst of our darkness, we need Him to shine light. Just a glimpse of His perspective on our chaos is so hopeful! He sees “a perfect pattern emerging and growing and alive-a living fractal”.
As I contemplate the complexity, splendor and depth of fractals, I see a parallel with our relationship with God. In Psalm 34:8, God’s word says, “Taste and see that the Lord is good.” Through our tragedy we have been learning that the more we taste of God’s character, His word and His promises, the more we experience His peace and the more hope we have for our future. He is an incredible God, with infinite complexity and yet infinite love for us. He IS trustworthy! With our human intellect, we know so little of what is to be explored about life and about God; we are really just scratching the surface. It is like looking at just the surface structure of a fractal and not “zooming in”. Fractals are indeed everywhere. They are in our body systems, our weather patterns, plants, water droplets, and snowflakes. They are the very essence of life; a window into the mind of God. Studying fractals reveals so much more complexity and beauty than what is perceived from the surface. In the same way, as we begin to search for God and get to know Him, we begin to get a taste of His complexity, beauty and love, and we crave for Him to reveal more of Himself to us.
As I began pondering fractals a couple of months ago, I was out for a walk one day and decided to listen to the soundtrack from the movie “Frozen”. I was surprised to hear reference to fractals in the theme song “Let it Go”!
“My soul is spiraling in frozen fractals all around
And one thought crystallizes like an icy blast
I’m never going back,
The past is in the past”
Isn’t it interesting how God uses such simple and everyday things of life to get His point across, to speak to our hearts? Sometimes He gets our attention in the most unusual ways. Not only was I intrigued to hear the word “fractal” in these lyrics, but I also thought about the line…”the past is in the past” and how that can be interpreted. When God forgives us of our past, however dark it may be, He doesn’t revisit it. Over and done…we are free to “Let it Go!” We no longer need to carry whatever burden it might be. On the same day that I paid attention to these lyrics, a friend “co-incidentally” (I put that in quotations since more often than not, these types of things are more like “GOD-incidences” rather than “co-incidences”) offered to me a “FRAKTAL”….an edible one! I had never heard of these! “I tasted and I saw” that it was indeed VERY GOOD! I quickly researched and contacted the company which I discovered is based in Aurora, Ontario. This company, after hearing about Amanda and her MD 2016 class, graciously donated 200 individually packaged “Fraktals” for our extended family at UOttawa. If you would like to “taste and see!” for yourself or find out more about “Fraktals”, visit http://www.fraktals.com/
If you have never heard of “fractals”, but are interested, here is a brief summary of some of the things that I have learned and a couple of helpful resources. The concept is very fascinating!
Summary of some things I have learned about fractals
“The term “fractal” was coined by Benoit Mandelbrot in 1975. It comes from the Latin fractus, meaning an irregular surface like that of a broken stone. Fractals are non-regular geometric shapes that have the same degree of non-regularity on all scales. Just as a stone at the base of a foothill can resemble in miniature the mountain from which it originally tumbled down, so are fractals self-similar whether you view them from close up or very far away.
Fractals are the kind of shapes we see in nature.” (http://whatis.techtarget.com/definition/fractal)
This video helped me to gain a better understanding of fractals: https://www.youtube.com/watch?v=xLgaoorsi9U
Jason Lyle, in his talk “The Secret Code of Creation”, refers to fractals as a “window into the mind of God…they are a secret code that God has built into numbers.” https://www.youtube.com/watch?v=nkwCl0ymTfg
Fractals are created using a mathematical formula. “Take a complex number, square it, and then add itself to the product, over and over again. Do it enough times, translate those numbers to colors and locations on a plane…you’ve got yourself a beautiful fractal!” http://www.mnn.com/earth-matters/wilderness-resources/blogs/14-amazing-fractals-found-in-nature
Fractals are everywhere in nature. Incredible order, infinite complexity and tremendous beauty is discovered when one zooms in on a fractal.
Mandlebrot helped us understand these shapes that God has built into numbers, with what has become known as a “Mandelbrot Set”.
A fractal: Mandelbrot Set Zoom: https://www.youtube.com/watch?v=0jGaio87u3A
All this to say, that God never ceases to amaze me! The more you look, the more He reveals. Thanks for coming along on this journey with me. I pray that in reading this, perhaps it will cause some deeper reflection on this Almighty and Faithful God of our universe. He has made Himself “discoverable” and He is searching for you! Do you want to seek Him? Matthew 7:7 says, “…Seek and you will find, knock and the door will be opened.” He wants to connect with you!
Two months before Amanda passed away, I memorized the following passage from God’s word. I leave this with you.
Ephesians 3:14–21Living Bible (TLB)
14–15 When I think of the wisdom and scope of his plan, I fall down on my knees and pray to the Father of all the great family of God — some of them already in heaven and some down here on earth — 16 that out of his glorious, unlimited resources he will give you the mighty inner strengthening of his Holy Spirit. 17 And I pray that Christ will be more and more at home in your hearts, living within you as you trust in him. May your roots go down deep into the soil of God’s marvelous love; 18–19 and may you be able to feel and understand, as all God’s children should, how long, how wide, how deep, and how high his love really is; and to experience this love for yourselves, though it is so great that you will never see the end of it or fully know or understand it. And so at last you will be filled up with God himself.
20 Now glory be to God, who by his mighty power at work within us is able to do far more than we would ever dare to ask or even dream of — infinitely beyond our highest prayers, desires, thoughts, or hopes. 21 May he be given glory forever and ever through endless ages because of his master plan of salvation for the Church through Jesus Christ.