Amy Hagemeier

Natural Patterns

Natural Patterns in Plants

 

Plants are everywhere. Plants are so common that they become very simple to overlook. When we walk down the street, we may fail to notice the trees down the median or the grass growing in the cracks of the sidewalk. These plants form an amazing world within themselves. Look carefully and see the veins scattering across the leaf. Count the flowers on a branch. Admire the beauty of all that randomness that is nature.

But is nature random? In some ways, nature is random. There is nothing that can precisely describe every example of a species. In the fact that each formation, each being, is slightly different is, indeed, random. However, there exists an underlying mathematical concept that can describe a random natural image surprisingly well. Plants are not exception. Though the mathematical match is not perfect, it is close enough to be considered valid as a description.

The web site http://www2.gvsu.edu/weesiesw/FGw.html discusses the role of fractals in plant modeling. The page contains a brief lesson on fractals, which assists in giving the reader some sort of understanding before diving straight into fractal images and wondering, "Did I miss something?" Also, we are told that fractal models are not the exact reality. This is because as fractals are magnified, they continue with same features. However, in nature, there is a limit to when the same features will show. In other words, if we keep magnifying a plant, the features will have to stop. There is a finite limit to how far nature can repeat a fractal-like pattern. At the end of the continuous magnification, we will find that we are left with atoms, of which all things are made. That is the limit.

This point is also emphasized on http://www.exeter.ac.uk/~ardalby/fractal.htm. The writer discusses the model of orchids, "They have this fractal like structure, but it is so fine that it acquires a multi-node existence. " However, on this page, he jumps into the terms "Aspect Experiment" and "Born probability model" without defining them for new readers. This is rather discouraging when trying to write a paper about the subject. What is preferred is the sight http://tqd.advanced.org/1270/msie4/discover/page4.html . They provide an image of a fractal fern, which was not found on the other sites. This page focuses on self-similarity. In the example of the fractal fern, "Each leaf is a smaller version of the entire fern. Then each leaf branching off that leaf is an even smaller one. This self-similarity continues forever." Then we are given an image of a real fern to compare with the fractal fern.

Other pages describe a pattern common in most nature and in some art. The site http://www.gordon-glasgow.org/fibonacci.html is a good page to find out what is so neat about the Fibonacci sequence. The author describes his first encounter with the sequence, "A Fibonacci sequence is a series of numbers beginning with 1 in which each number is the sum of two previous numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, etc. Like I said, interesting, but so what?" The site discusses the spirals on a sunflower’s head, pinecones, and pineapples. He notes that on a sunflower, there are 21 spirals going one way and 34 going the other. On a pinecone, the spiral numbers are 5 and 8. The pineapple has 8 and 13. They are all consecutive numbers in the Fibonacci sequence.

A site less concerned with consecutive numbers in the sequence than having the plant containing one number in the sequence is the site http://riceinfo.rice.edu/armadillo/Vanishing/j.Coming.of.the.Corn/j.natures.patterns.i. This page contains a project for younger individuals interested in the Fibonacci sequence. This page mentions pine cones, flower heads, and leaf patterns, but there is more focus on the fact that monocotyledon plants usually have 3 petals (or multiples of 3) and dicots usually have five petals (or multiples of 5). Three and five are consecutive numbers in the sequence; however, the page did not seem to be emphasizing that fact.

Finally, on http://www.mcs.surrey.ac.uk/Personal/K.Knott/Fibonacci/fibnat.html#plants, the author gives examples of where the Fibonacci sequence can be found in plants. He mentions, like the previous page, petals on flowers, "…some delphiniums have 8; corn marigolds have 13 petals, some asters have 21…" He discusses seed heads, pine cones, and leaf arrangements. He crams more examples in his pages and includes many links to these examples.

On my web search, I found many pages dealing with fractals (though it was more difficult to find pages discussing fractals and plants) and the Fibonnaci sequence. However, Dr. Lega described to me the lines running down the side of some cacti are similar to the ripples in sands. After much disappointment in using search engines to explain why this happens, I gave myself the task to photograph these stripes and to try to give reasons why these stripes occur.

Photograph #1 is of two saguaro cacti outside the Old Main building on the University of Arizona campus. The cactus to focus on is the one in the center of the photograph. Here, the stripes Dr. Lega mentioned are clearly visible. Starting at the base of the saguaro, the stripes, continuing upward, sometimes tend to split.
This split is better seen in photographs #2 and #3. In photograph #2, the split occurs on the ridge. That is, where the stripe of the saguaro protrudes from the cactus toward us, a split happens, and there is one more stripe on the cactus than there was before the split. Photograph #3 not only has the split occurring at the ridge, but there is also a new stripe emerging from a valley on the cactus. The valley is the indention between the ridges. Again, this leads to the addition of a stripe where before there was none.

Photograph #4 shows us a defect-ridden saguaro, also outside the Old Main building. The defects at the bottom of the photograph appear at about the same rate that the defects on the other saguaros appear, but the top of the cactus in #4 seems almost cancer like in the way it spreads out in all directions. The top is loaded with defects. Following the stripes up the cactus reveals that most of the defects occur with the addition of a stripe rather than the elimination of a stripe. In fact, outside of cactus #4, the other saguaros depict the defects that develop with the addition of a stripe. Dr. Lega does have a photograph of a cactus with two stripes that come together to form one (whether the stripes are ridges or valleys, I cannot remember). Photograph #5 is a closer look at the body of the saguaro in #4.

Why is the increase in stripes preferred over the decrease in stripes? Perhaps the reason for this preference is due to the growth of the cactus. As it grows, the body becomes wider. If the number of stripes remained static, the width of the stripes would increase and the surface of the cactus would become more smooth. This might not be favorable for the survival of the cactus, as its flesh would be more exposed than if there were valleys and ridges, on which the needles of the cactus are situated. A way to keep consistent with survival and growth would be to simply add another stripe. Looking again at photograph #1, many of the defects occur at the bottom of the saguaro, which, in this case, is the thickest part of the cactus. Where the cactus is becoming thinner, there are no signs of defect. This is not always true, though, just as not all the defects occur with the addition of a stripe. Some delete a stripe, but why are deletions not as common? Perhaps the increased protection from an extra valley or ridge is not necessarily worth deleting. Perhaps it is similar to the fact that though we are suppose to be born with ten toes, others are born with some other number. The fact that there is a closing of a ridge is a little mutation in the nature of the defects.

Stripes also occur in the internal structure of the saguaro. When a saguaro dies, its internal support dries and reveals another stripe pattern. This pattern, though, has little to do with the extrinsic patterns of the saguaro. It would be interesting to see how the internal stripes are situated and at what time they split during the growth of the saguaro or to determine if these factors are even related to each other.

Some scientists believe that stripes in animals occur due to evolution. The stripes assisted the animal in survival, so the animals with stripes propagated. Then others bring up the fact that stripes on mollusk shells seem to have no attachment on survival whatsoever. Looking at the cactus, I am more lenient toward the idea that perhaps the stripes exist due to evolutionary reasons. However, there can be another reason as to why the valleys and ridges are favored over other possible security measures the cactus could have adopted. These other reasons seem to be what scientists studying patterns are looking for. What reasons governed by means other than evolution can explain the patterns seen here? Is it embedded genetically from the beginning? Is it favored by some other means, some other force in nature? Why did nature choose this design over another? Answering these questions will not just help figure out the mystery behind the stripes in cacti but patterns in all different areas of nature.