Yesterday I mentioned that the leaves of the dragonfruit seemed to be arranged with spiral symmetry. If one looks at the leaves in groups of three, they seem to be arrayed as shingles on a roof or scales on a fish. In fact another name for dragonfruit is ‘dragon scales’.
I thought that I would be able to demonstrate the overall spiral symmetry of the dragonfruit (DF) by looking at this fruit from the bottom.
I am afraid that I wasn’t able to capture this. The above watercolor sketch is actually mixed media, since I used pencil to outline most of the DF leaves. The grayish-beige area that includes some pencil shading, is actually the center of the fruit, where it is detached from the cactus plant on which it grows.
Not seen in the above view of the DF, is the hexagonal shape from which triangular leaves jutting out from the surface. These leaves, exiting the 2-dimensional surface of the DF (discounting the curvature of the fruit), disrupt a clear view of the hexagonal and spiral symmetry. They break up the visual symmetry.
[This analysis of the DF brings to mind Flatland, which I discussed in an earlier post, in which Edward Abbott, the author writing under the pseudonym ‘A. Square’ described a land of two dimensional creatures, which could not conceive of a third dimension. Is the dragonfruit an inter dimensional fruit?]
One can see a much clearer example of hexagonal elements in the photograph below:
There is nothing to disrupt the visual symmetry in the pineapple. The hexagonal elements are arranged diagonally, which suggest a spiral symmetry.
It would be interesting to see if the repetition of hexagonal shapes in the pineapple and the DF are common to fruit of other plants. Would that mean that the other plants are related to one another in some way? Is there a common ancestor from which the hexagonal shapes originated? Is there a bit of genetic code that is common to them all?
Hexagonal shapes are not restricted to the plant kingdom. They are also found in honeycombs, structures built by bees. How did this come about?
Interesting to ponder. If anyone has thoughts about this, I’m interested to hear.