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"The unique properties of the Golden Rectangle provides another example. This shape, a rectangle in which the ratio of the sides a/b is equal to the golden mean (phi), can result in a nesting process that can be repeated into infinity — and which takes on the form of a spiral. It's call the logarithmic spiral, and it abounds in nature."
While my wife hunts for sea glass along the shoreline, I'm usually drawn more to the beach pebbles. I'm attracted to the variety of colors and patterns, and to holding one in my hand and knowing that each one is the expression of physical processes that may have begun deep in the earth or deep in the ocean. We gathered these stones on Rodeo Beach. I placed them on the sand and enjoyed the colors but didn't care for the shape I'd made. My wife rearranged them into this spiral.
Also found along the beach were these varied hues of layered serpentine, chert and other minerals. The original image is 24x53 inches. Shot with 105mm lens, I focus-stacked each vertical frame, then stitched the six resulting frames into a panorama.
My favorite stone was this interesting little pebble with patches of what I thought at first glance might be rose-colored quartz. Looking at it under a 10X hand lens, though, the reddish color looks like it could be embedded chert. In any event I enjoy the complexity of its construction and thinking about its formation over perhaps millions of years. (Then again, if you think about it, everything from the pebble to the fingers that picked it up off the beach, began to form at the very beginning of time itself.)
I photographed the pebble in a small abalone shell that brought me back to my wife's spiral on the beach and to thoughts of a nautilus shell she has at home. The nautilus is often used to describe the correlation between the Golden Ratio in art and architecture, and Fibonacci numbers in mathematics -- places where spirals are found.
The spiral is an interesting shape, expressed in nature from molluscs to galaxies, in art from petroglyphs to Andy Goldsworthy. Water spirals down the drain in our sink and spins into hurricanes over the ocean. Spirals occurred in sacred form from the Celts to the Aztecs. They are hardwired into our DNA and even occur, in a manner of speaking, in the depths of our psyche.
I photographed the pebble in a small abalone shell that brought me back to my wife's spiral on the beach and to thoughts of a nautilus shell she has at home. The nautilus is often used to describe the correlation between the Golden Ratio in art and architecture, and Fibonacci numbers in mathematics -- places where spirals are found.
The spiral is an interesting shape, expressed in nature from molluscs to galaxies, in art from petroglyphs to Andy Goldsworthy. Water spirals down the drain in our sink and spins into hurricanes over the ocean. Spirals occurred in sacred form from the Celts to the Aztecs. They are hardwired into our DNA and even occur, in a manner of speaking, in the depths of our psyche.
"The way to the goal seems chaotic and interminable at first, and only gradually do the signs increase that it is leading anywhere. The way is not straight but appears to go round in circles. More accurate knowledge has proved it to go in spirals: the dream-motifs always return after certain intervals to definite forms, whose characteristic it is to define a center.... The development of these symbols is almost the equivalent of a healing process. The center or goal thus signifies salvation in the proper sense of the word."
--Carl Jung from Psychology and Alchemy
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