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.
Lots of natural occurrences of Spirals in plants. See (e.g.) here: http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html#plants or here: http://www.popmath.org.uk/rpamaths/rpampages/sunflower.html
Hexagons: just google:
& click “images” – there’s zillions!
There’s only three regular shapes that can “fill a plane” – triangle, square and hexagon; of these the hexagon has the smallest “edge/content” ratio so it’s more ‘economical’ in many ways.
Like the pics!
Thank you for your comment, Roger. I love the Fibonacci series!
I’ll have to look at the Dragonfruit again. If it has only five sides, maybe the leaf extension was it’s solution to the edge/content ratio!?
It would be interesting to understand if there is a common genetic sequence for symmetry in plants.
Fantastic pictures and discussion – I’m really enjoying this. By the way, don’t suppose you tried opening up your dragon fruit did you? It’s a bit of a surprise. But it has nothing to prompt more reflections on symmetry I’m afraid – more a discussion of chaos! I think you would need your titanium white anyway.
Thank you, Woman Unadorned. Opened dragon fruit is on the agenda for next post!