Monday, March 26, 2012

...fractals, fossils, and me

I do not believe in time. I like to fold my magic carpet, after use, in such a way as to superimpose one part of the pattern upon another. Let visitors trip. And the highest enjoyment of timelessness-in a landscape selected at random-is when I stand among rare butterflies and their food plants. This is ecstasy, and behind the ecstasy is something else, which is hard to explain. It is like a momentary vacuum into which rushes all that I love. A sense of oneness with sun and stone. A thrill of gratitude to whom it may concern-to the contrapuntal genius of human fate or to tender ghosts humoring a lucky mortal.

I encountered this cactus in Tempe, Arizona in January. The pattern, color and texture are enough to make an art major weep...or at least sigh. But, in my reverie, I still managed to point my iPhone and snap a photo. Of a fractal. 
Best simple definition I’ve found of a fractal is this, from Wired: 
From sea shells and spiral galaxies to the structure of human lungs, the patterns of chaos are all around us. Fractals are patterns formed from chaotic equations and contain self-similar patterns of complexity increasing with magnification. If you divide a fractal pattern into parts you get a nearly identical reduced-size copy of the whole.
The mathematical beauty of fractals is that infinite complexity is formed with relatively simple equations. By iterating or repeating fractal-generating equations many times, random outputs create beautiful patterns that are unique, yet recognizable. 
I repeat, this is a simple definition. Let’s bypass Dr. Math - “fractals possess a non-integer dimension” - and give short shrift to Mandelbroit sets and mathematical visualization. I am, after all, (refer to paragraph one) an art, albeit, a redundant one.
My inner geek, however, shifted into high gear on a recent hike at Point Reyes. On the long trek down to the lighthouse, I glanced at the rock formation to my right. I cannot recall the geological era but the exposed rock was once seabed many, many million years ago. After the trip, I found a field guide on the web ( that revealed this bit of interesting information: 
This rock (Point Reyes conglomerate) can be seen in exposures on the peninsula's headlands. Particularly good exposures can be seen in the exposures around the visitor's center for the lighthouse. These rocks are quite convincingly correlated with the Paleocene turbidites (Carmelo Fornation) found well exposed in the Pt. Lobos Marine Reserve south of Carmel, California and may well have been directly adjacent to Carmel during their formation some 50-60 million years ago. Recent studies...indicate that 60 million years ago Pt. Reyes was attached to the west of Monterey, California where similar Salinian granitic rocks are common. Fault movement along a large, largely offshore, fault of the San Andreas System is believed responsible for moving Pt. Reyes from this location.
I don’t know how familiar you are with California geography but Monterey is a far piece from Marin County. Once more, however, I digress...back to what caught my attention. Check this picture.

Yep, that’s a fossil. If you squint a bit, you can see a shape in the rock...a bit spirally, like the chambered nautilus in the photo to the left: pilfered from The moment took my breath away. I wasn’t in some museum, simply out for a Sunday stroll when I encountered this “hello” from the past. Standing on land that was once underwater somewhere between Carmel and Monterey. Thinking on such a thing makes me giddy.  A fractal fossil at eye level. 

I had encountered a more ephemeral reference to fractals several years ago in William Young’s book, The Shack. Mack, the central figure in the book, meets Sarayu (the Holy Spirit) in this passage:
Papa then arrives. Mack says how, though the garden is a mess, he somehow feels strangely comfortable in it. Papa and Sarayu smile at each other. Sarayu says, “And well you should, Mackenzie, because this garden is your soul - this mess is you! Together, you and I, we have been working with a purpose in your heart. And it’s wild and beautiful and perfectly in process. To you it seems messy, but to me, I see a perfect pattern emerging and growing and alive - a living fractal.” Mack crumbled. He looked at his garden and it really was a mess, but incredible and wonderful at the same time.
Twenty years have passed since I first visited Point Reyes. The lighthouse was closed to visitors that day but I ventured down the path to a spot where I saw a plant. Just one, a determined lithophyte that grew out of the rock’s striated, polished surface. I took a snapshot and forgot about it until the film was developed. The image was lovely, a bit of abstract art. The swirly, smooth stripes behind the plant looked just like the ones I saw in a book about - you guessed it - fractals. The photo was lost in the Great House Debacle of 2002 but the memory hasn’t faded. 
I thought of that hardy plant on my latest trek. And encountered it again, two decades later. Here’s the latest photo:
The smooth surface is now cracked and crumbly, not the rock that I remember. The plant is a bit stalkier, its roots more exposed. Notice it’s a red-head: headstrong and sassy, suited for life on the edge of the Pacific headlands. 

The photo with it's busy backdrop lacks the abstract quality of the first. But one good polish and the fractal swirls will reappear. That polish will take eons, of course, and who knows what life will co-exist with the firmament. 

The whole cliff, which straddles the San Andreas fault, might once again rest underneath the ocean. Or perhaps travel farther north near Mendocino (at least, where it is now) or beyond. Time will tell...long after I am no longer a distant memory. 

All I know is that, like Mack, underneath my broken, messy bits and bobs lives “a perfect pattern emerging and growing and alive - a living fractal.” I am a wonderfully made mess. Oh, what a beautiful morning!


Charles Van Gorkom said...

Going the other way,
a fractal is the fractal
of a fractal,
which is the fractal of a fractal.
Follow it all the way back
past the galaxies
if you can,
by faith if you can't,
to the mind of God.

Celeste said...

This should have been the entire post...

GretchenJoanna said...

Celeste, these are gorgeous nature photos. Point Reyes is on our family favorites list of places to go, but I've never paid attention to the things you noticed and thought about.

Your last photo, of the succulents perched in the rock like a couple of lanky birds, is my favorite of the bunch. I do love succulents.

Celeste said...

So do I! I had my own little pot of hen n'chicks when I was a young girl. Spent time this past weekend browsing a huge rack at the garden shop...ready to prepare a dish garden for the back porch.

Easter blessings, Gretchen Joanna!