I found some cool compositions in this abandoned scrapyard near downtown Albermarle, North Carolina. After squeezing myself, and equipment, through a narrow opening in the building (3rd image below), dozens of mosquitoes descended on me in an instant. I had to get my shots and get out quick!
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As a follow-up to my previous Sunflower Study Part 1 post, here are more compositions along with a continued discussion about the amazing growth enabling mathematical structures consistently found in nature.
The foundation of this structure is the Fibonacci Numbers or Sequence. Start with 0 and 1 and then the sum them, drop the zero and you have the first two sequence numbers (1, 1). Then keep summing the the two numbers to build the sequence – 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 and on. If you divide any number by the previous number you get 1.618 – the Golden Mean, or phi φ.
Next, consider a 360° circle. If you divide 360° by 1.618 you have an angle of 222.5°. The remaining angle in the circle is 137.5° – the Golden Angle (360° – 222.5°). If we build a model of square boxes, each with an adjacent box based on the Fibonacci Sequence, then and any two adjacent boxes will form a Golden Rectangle. Drawing an arch across the outer corners of each box forms the Fibonacci Spiral or Golden Spiral. Now we have the mathematics and geometry to reference what can be seen throughout the natural world.
The term phyllotaxis refers to the botanical study of phylla (leaves, seeds, flower pedals, etc.) on plants. A plant will typically set each phylla at a 137.5° “golden” angle from the previous one. This creates a “golden” spiral of leaves up the stem or seeds around the center of the flower. This enables not only the maximum possible exposure to the sun, but also the most efficient use of space. Fibonacci Spirals are a visual consequence or patterned observation based on this arrangement.
When observing the pattern of disc florets in the sunflower, it’s usually easy to see the both clockwise and counter clockwise spirals. On a typical medium size sunflower you can observe 34 spirals in one direction and 55 spirals in the other. Larger sunflowers can have spirals of 55 and 89. Did you notice these are Fibonacci numbers? John Edmark, a professor at John Hopkins University, is also an artist and inventor. Check out this wonderful video about his fascinating work based on Fibonacci spirals. Another great video about these amazing mathematical structures is Nature by Numbers, it shows a great animation on the distribution of sunflower disc florets.
Once you start looking for the golden spiral, you’ll find them all around you! And, if you’re like me, you’ll get a sense of awe and closeness with our Creator. Perhaps in the future, I can create some compositions to support a discussion around the Golden Mean. These compositions can be best viewed by clicking to see a high resolution version from my portfolio site. Thanks for taking time to visit my blog.
For the past several weeks, I’ve enjoyed the sunflower plantings on my route to work each day. Last week I decided to stop and capture these wonderful flowers in their morning glory. This post, and the next, feature several different visual approaches along with some very interesting tidbits about the common sunflower (Helianthus annuus).
Each plant will typically bears one or more large, wide flower heads (capitula). The flower head is actually a compound flower. The outside consist of bright yellow ray florets, while the inside disc contains yellow orange disc florets. In the photo above and below, you can see at the center, the zone of unopened disc floret buds. Just outside the unopened zone, you can see the next zone of new disc florets in their male pollen phase. Here is where the bumble bees are most active. After a few days, the disc florets enter their female phase. They extend in the third zone out to the edges of the flower disk.
When the flower blooms, all the disc florets are unopened, tiny buds. The disc florets first open in their male phase on the outside of the disc. Over several days, the male phase disc florets seem to move as a wave towards the disc center. During the growing period, sunflowers will tilt during the day to track the sun. As the flower begins to bloom, this tracking will stop. Once the flower matures, they will generally face the east. I was amazed when I read about this. My route to work runs from east to west; so I really noticed these east facing flowers in the morning as I traveled west.
One of the most fascinating features of the sunflower is the method in which the disc head uses to disperse disc florets. From the center of the disc, a mathematically brilliant spiral technique packs the maximum number of disc floret buds across the surface area of the disc head. This spiral is known as the Fibonacci Spiral, which in turn is based on the Fibonacci Sequence. I wrote about this in my An Elegant, Intelligent Designpost. Perhaps I’ll discuss it in more detail in the second part of this post.
This series was shot with my Nikon 28mm – 300mm lens, using manual focus. Several times, I had to slightly lean back when I reached the minimum close up focus point. Perhaps I’ll try renting a macro lens in the future. I appreciate you stopping by today. For the best viewing experience, click on an image to see a high resolution version.
The east end of Ocean Isle Beach remains undeveloped and retains much of the characteristics of a southeastern US barrier island. This seascape is forever changing, and each time I visit, there is some new to discover . Below is a view of a tidal pool looking from the Intracostal Waterway side of the island back towards the seaward side.
Below is a sunrise view looking east towards Holden Beach, another North Carolina barrier island.
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The southern live oak, quercus virginiana, is a large majestic oak tree species native to the southeastern United States coastline. While some other species are loosely referred to as live oaks, the southern live oak is an iconic part of the Old South. The term “live” refers to the tree’s evergreen characteristic – its leaves remain nearly year-round. Over a period of days, leaves fall off in the spring as new leaves begin to emerge.
The tree is anchored by a deep tap-root which develops into an extensive root system. Lower branches will reach out to the ground and then turn upward. These features, along with a low center of gravity, allow southern live oak to withstand strong sustained costal winds – hurricanes. Several live oaks have been certified to be over 1000 years old!
It prefers well drained sandy soils below 300ft above sea level. Their broad, dense canopy discourages flammable undergrowth. As such, the tree can usually withstand fires because the flames are unlikely to reach the crown. If burned, the crown and roots respond with vigorous growth.
Though not suitable for planking, the live oak’s hard, strong and curved wood was a preferred source of sailing ship framework timbers. The frame of the famous USS Constitution was constructed from southern live oak harvested from the state of Georgia. The density of wood grain helped the ship survive cannon fire during The War of 1812, earning it the nickname “Old Ironsides”.
Today, the southern live oak provides shelter and food to local wildlife. I captured this series, including the white tail bucks above foraging for live oak acorns, on the Intracostal Waterway near Holden Beach, North Carolina.
Earlier this summer, I attended the wedding of a friend and fellow Scout leader in Danville, Virginia. After the reception, I had the opportunity to visit the local tobacco warehouse district, near the Dan River, which is into it’s initial phases of urban renewal – the Danville River District. The late afternoon afforded some nice lighting. I plan to return soon to shoot in the early morning light.
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