The golden ratio tends to show up in natural forms and processes. In nature, golden ratio in plants is very common. The golden ratio solves mathematical problems of close-packing, and also appears when there is recursion, or five-fold symmetry. Basically, the golden ratio is a go-to when it comes to efficiency in plants. It also happens to be super lovely!
Ways to See Golden Ratio in Plants
Since the golden ratio crops up in unexpected ways, I typified 3 distinct ways it shows up.
Type A. Golden Spiral (petals, leaf arrangement)
Like the snail shell, you can see a golden spiral when the rungs get wider as you go out. When the spiral is acting up and down on the stem, the leaves point out to the golden angle, so they are varied enough to catch light. The radius will always increase with respect to the amount the previous cycle increased.
Type B. Fibonacci Numbers (petals, seed arrangement)
A number of flowers have a golden spiral arrangement of petals, which, when counted out individually give Fibonacci numbers, signaling a discrete spiral. This is because when the structures form, they behave just like rabbits unstifled in a meadow. One pair gives rise to another pair, and each pair gives rise to another once they mature. (Read more about the rabbits.) The numbers that result include:
1,2,3,5,8,13,21,34,55,89,144,233,377, 610, 987, 1597…
When I say Fibonacci numbers, I mean any of those.
Type C. Pentagonal Symmetry (petals, fruits, seed pods)
Whenever we have pentagonal symmetry, we have the golden ratio segments. Pentagonal symmetry had the same self-similar components as a pentagram star. You can read more directly about the pentagonal archetype as well as rotational symmetry to understand this.
12 Examples of Golden Ratio in Plants
There are more mays golden ratio can show itself, such as branching structure, but these are all the ways golden ratio shows up in these 12 plants shown here. See the examples, flowers, leaves, seeds, seed pods, and fruits.
1. Marigold petals
The petals of the marigold form in a golden spiral, so as they get farther from the center the radius becomes wider. This allows the flower to make its characteristic, pom-pom shape, which we’ll see with other examples below. Marigold flowers exhibit both golden ratio type A (golden spiral) and B (Fibonacci numbers) in the numbers of petals. These two often go hand-in-hand.
2. Pinecone shingles
The pine cone makes a spiral with its shingles the same way the marigold does with its petals. As far as counting the Fibonacci numbers, these measurements are done by counting every shingle on the pinecone. For large pinecones with may be time-consuming, but certainly easier than the marigold. Off the tree, with no shingles eaten or damaged, the pinecone has a Fibonacci number of shingles, usually over 55.
The pinecone thus exhibits both type A (golden spiral) and type B (Fibonacci numbers). Note that often the spirals are not concentric circles in which you can count each rung, but descend into larger and larger radii as it progresses.
3. Succulent leaves
Succulent lobes are a great way to count out the structures. As long as no lobes have fallen off, a complete succulent plant will have Fibonacci number of lobes. You can also see golden ratio in succulents when they have leaves on a stalk. The spacing between the leaves will be staggered, and the golden and separates them. Read more about golden angle in my golden ratio explained post.
Like the majority of examples of golden ratio in plants, succulents tend to exhibit a combination of golden ratio type A (spiral) and type B (Fibonacci numbers).
4.Sunflower seed pods
Sunflower centers are strikingly beautiful, and the reason is probably the maturation of the golden ratio process. It is allowed to go out dozens and dozens of Fibonacci numbers, while maintaining the spacing that allows one seed to fit between the others before it, and so on. The resulting pattern is striking and most similarly resembles the well-known krystal spiral.
Sunflowers are also a group of species (helianthus) that has many variations in different climates and parts of the world. Many areas have their own “wild” sunflowers, such as the beach sunflower and Mexican sunflower. In the sunflower head, we see golden ratio type A. In the numbers of petals and seed pods, we also see golden ratio type B.
5. Pineapple patterns
The structure of the pineapple is also greatly influenced by golden processes. The segmentations of the fruits on its angled array follow a golden spiral pattern and, you guessed it, contain a Fibonacci number of segments (golden ratio type A & B). Notice that the segments are not in a tidy grid, but actually twist around the fruit.
6. Fern fiddleheads
The fern fiddleheads unfurl as they first form, before putting on leaves. The fiddleheads form in a snail-shell type spiral, a golden spiral. This is golden ratio type A, a golden spiral. The shape is really striking in the absence of many other features besides tiny hairs. The fiddle head is edible and nutritious.
7. Starfruit shape
The shape of the starfruit has pentagonal symmetry: it can be rotated 5 times to create congruent forms. The star shape of the starfruit endows it with golden ratios amongst its parts. For example, ratio between the arms and distance between the points are self similar. Read about how to get the golden ratio formula to learn more about the recursive property. The starfruit thus shows golden ratio type C, pentagonal symmetry.
8. Morning Glory
Similar to the starfruit, the morning glory flower has pentagonal symmetry amongst its conjoined petals. This is the first flower on the list showing golden ratio type C, pentagonal symmetry.
Five-fold symmetry invokes the golden ratio because many of the proportions within the raw shape have the recursive property. For example, the ratio from a long part to a short part is the same as the ratio of the short part to the long minus short part. (See the math.) For many parts that don’t happen to fit this, this golden ratio squared is invoked instead.
9. Cauliflower, romanesco, and cruciferous vegetables
The fractal appearance of cauliflower, romanesco, cabbage, broccoli, and nearly every other cruciferous vegetable is due to the space filling fractal processes. You can read more about how space-filling fractal structures come from five-ness. The cruciferous vegetables are showing golden ratio type A, spiralization.
If you’ve ever cut into a cabbage through the center and marveled at the way the leaves pack in on each other, that’s due to the space-packing efficiency of the golden ratio at work.
10. Roses: thorns, leaves, and petals
Roses are another triple threat of golden ratio punch, having the thorns, leaves, and petals all arranged this way. Thusly roses show golden ratio type A most outwardly.
It is commonly believed that roses have been cultivated by humans for over 5000 years beginning in Asia. According to fossil evidence the rose is 35 million years old, in other words, about as old as they come. Rosewater was even used as currency in the 17th century. So people recognized the significance as its beauty translated into medicinal purposes.
11. Hibiscus shape
The hibiscus flower also has leaves following the same golden angle pattern (most plants actually do this, start looking!) But, more notably, the hibiscus has a pentagonal symmetry with its five petals. Many medicinal tea flowers and flowers that give edible fruits have the five petalled configuration.
12. Dahlia petals
This flower is one of the most striking examples of golden ratio type B, countable Fibonacci numbers. Like the marigold it creates its petals in a spiral the way rabbit reproduce in a field.
The spacing between the petals also exhibits golden ratio type A. (Type B is rarely unaccompanied.) The size and shape of the dahlia petals themselves are what end out in this rounded pom-pom shape. The marigold, the first on this list of golden ratio in plants, has the same pattern with a different style of petal.
Golden ratio is inescapable in nature
The golden ratio is ubiquitous in nature, and indeed this is only a subset of the examples available. I also have written on 10 examples of the golden ratio in ANIMALS. Stay tuned and we will readily have whole articles on golden ratio in flowers, golden ratio in fruits, and in seed pods alone. Which example did you find most beautiful? COMMENT BELOW. (Or else.)
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Is there a way to grow vegetables using the golden ratio for optimal nutrition and how to have beehives with healthier bees and more nutritional honey?
We can probably find out with experiments. I like the idea of an herb spiral, some also set up electroculture wires but I think those could be cancelling out the more natural fields. Check back and I’m actually publishing about the quacks that do this