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What do Caly and pineapples have in common?

January 18, 2019

If you answered they are both from Hawaii, sorry but pineapples are from South America!


Ok, another clue: What do Caly, pineapples and spiral galaxies have in common?

…The answer is that they all exhibit a geometric pattern called a golden spiral (or Fibonacci spiral). For plants, what is special about this arrangement is that it leads to efficient packing of seeds as seen in pine cones and florets in sunflowers.


The other reason this pattern is very important for plants is that, because it arises from seeds, florets or leaves growing in intervals determined by the golden angle which is an irrational number (i.e., a number that can't be written as a ratio of two integers, like pi), leaves growing around a stem using this pattern will rarely grow directly above older leaves below. Consequently, this golden spiral pattern leads to a very efficient way to minimize light competition among leaves on the same plant!



Looking at the positions of the leaves and the leaf scars along Caly’s stem, you can see the spiral  pattern.


This is quite a big deal for most of Caly’s family as nearly all genera and species of Hawaiian Lobelioids have a whorl leaf arrangement. Even Brighamia insignis, Caly’s famous cousin, have this clear spiral leaf arrangement!


Now, if like us you think these Fibonacci spirals in plants are awesome, allow us to indulge on the most complex (and delicious) one we know of: the fractal-three-dimensional-Fibonacci spiral, aka, the romanesco broccoli!


In fact, just based on the golden angle alone we can replicate this beautiful plant pattern based on a few lines of math and code…


Who knew plants had to know so much math to grow??


ps- For plant/math/coding nerds, the r code to generate the 3d graph is attached here.

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