# Blog Archives

## Nature’s Patterns

*By Bruce Rottink, Volunteer Nature Guide and Retired Research Forester*

At the most basic level, the universe is orderly, although sometimes that order is not immediately apparent. Albert Einstein famously remarked, “God does not play dice with the universe.” Fortunately, in the forests of Tryon Creek State Natural Area (TCSNA) we have many wonderful examples of the orderliness of the universe. For this article I will focus on the symmetry that we see in so many of the organisms in the forest.

The most common types of symmetry we can see at TCSNA are typically referred to as spherical, radial and bilateral symmetry. Another way to think about these kinds of symmetry is symmetry around a point, symmetry around a line and symmetry around a plane.

*Spherical Symmetry (Symmetry around a point) *

With spherical symmetry, there is one point in the middle of an object, and no matter which direction you go from that point, everything is the same. If you’ve already guessed that all the examples are spheres, you’re right! The seeds and fruits of some plants are the best examples of this at TCSNA. For example, the picture below shows the fruit of a bedstraw (a.k.a. “cleaver”) plant (*Gallium* spp.) The scar in the middle of the picture is where the fruit was attached to the stem.

Other forms of symmetry get a little more interesting.

*Radial Symmetry (Symmetry around a line)*

A second type of symmetry is radial, where there is a central axis to the object, and the parts all stick out equally in any direction from that central axis. One of the best examples can be seen in this mushroom fruiting body. Imagine the red dashed line going down the center of the stem of the mushroom. At a given distance from the ground, if you travel out at any 90° angle to that red line the mushroom structure is identical.

The picture below is of the underside of the mushroom’s cap. I’ve put in a red dot to indicate the central axis of the fruiting body. No matter which direction you look out from the center, the structure looks essentially the same. The edges of the gills that you see as lines, all point to the center of the mushroom.

Looking at the underside of the mushroom’s cap provides an additional perspective on radial symmetry.

* *

* *The mushroom above is an example of the simplest kind of radial symmetry. But radial symmetry can be more complicated, *and more interesting*.

*Spirals – A special case of radial symmetry*

The mushroom pictured above is a very simple example of radial symmetry, but more complex examples can be easily found at TCSNA. The most obvious are some of our native conifers. For example, at first glance the scales on a Douglas-fir (*Pseudotsuga menziesii*) cone might appear to be arranged in a random pattern.

In fact, the scales on a Douglas-fir cone are arranged in a definite spiral pattern around a central stalk. The scales are actually arranged in __multiple__ spiral patterns. To illustrate this I painted the bracts (the three-pointed papery structure attached to each cone scale) to highlight these spirals. Each spiral is a different color. The results can be seen in the movie below. Since each cone scale is actually part of three different spiral patterns, I have painted three different cones, each illustrating one of the three patterns. A different color of paint was used to mark each of the spirals. Watch first one cone and then the others to see these three different spiral patterns.

You can see in the movie that there are a set of __three__ spirals of cone scales going in one direction around the cone axis at a very gradual angle. There is a second set of __five__ spirals going around the cone at a steeper angle in the opposite direction. Finally, there is a third set of __eight__ very steep spirals going about the cone in the same direction as the first set of spirals. So each scale is part of all three spirals going around the cone’s central axis.

In any given plant, the number of spirals are a part of a set of numbers known as the Fibonacci sequence of numbers. The Fibonacci numbers were described by an Italian mathematician more than 800 years ago (and Indian mathematicians had apparently described them even before that). Starting with the number 1, each subsequent number is the sum of the two previous numbers. Below is the start of the original Fibonacci sequence (the “modern” version starts with zero, which has no impact on the rest of the sequence):

1, 1, 2, 3, 5, 8, 13, 21, 34, etc, etc, *ad infinitum*.

In the botanical literature, it is traditionally reported that the number of spirals in any plant are always __two__ consecutive numbers of the Fibonacci sequence. With one exception. The pineapple fruit is almost always described as having __three__ spirals. I present here the possibility that the Douglas-fir cone, like the pineapple, is composed of three spirals, not the traditionally recognized two. But, whether it’s two spirals or three, it represents an example of order in nature.

*Bilateral Symmetry (Symmetry around a plane)*

Finally, there is bilateral symmetry, which is symmetry with respect to a plane (think of a sheet of glass). The structure is identical on both sides of the plane. The butterfly below is a beautiful example of bilateral symmetry. Think of an imaginary sheet of glass running vertically through the butterfly’s body. Each side of the body is an identical mirror image of the other side. The easiest feature to see in the photo below are the patterns on the wings.

Plants often exhibit bilateral symmetry, as exemplified by the bigleaf maple (*Acer macrophyllum*) fruit shown below. In fact there are two different planes of symmetry. The first one is centered around the red line drawn on the picture. The second plane of symmetry is represented by the paper on which this picture could be printed. The front and back sides of the seed are identical.

*But wait… Not everything in the forest is symmetrical!*

My favorite example of a non-symmetric organism in the forest is the banana slug **(***Ariolimax columbianus***)**. Below are two pictures of the same slug. One picture is of the right side of the forward part of its body, and the other is of the left side of the forward part of its body. As you can see, the slug only has one breathing hole, and it is on the right side of its body. Thus, the slug does __not__ display symmetry in this regard, it is asymmetrical. Every slug has its breathing hole on the right hand side of the body.

But that’s not the only way a slug is asymmetrical! Look at the coloration on the body of the slug pictured below. A black spot on one side of the slug is not matched with an equal sized, or shaped black spot on the other side of its body.

*Why symmetry?*

Symmetry is often useful, such as birds having one wing on each side of its body. Imagine a bird trying to fly with both wings on the same side of its body. But In truth, while nature has intended many things to be symmetrical, oftentimes the symmetry is not perfect. These imperfections may result from mutations during development, or accidents. So what you ask? Scientists have discovered that some animals, like female peahens and barn swallows, prefer males with symmetrical tails. To the birds, symmetry could be proof of a potential mate’s normalcy, which is often the safe choice.

The symmetrical patterns that we see in much of the flora and fauna of TCSNA provide some reassurance in the orderliness of the universe. It suggests that perhaps Einstein was correct!