Figure 4:

Photo by: Kathryn Schottl
Figure 5:
However, flower petals are not the only source of the Fibonacci sequence in nature.
Seed heads are another place to spot the Fibonacci sequence in nature. Seed heads tend to
form spirals just as with the petals this is for efficiency, the seeds grow from the middle pushing
the other seeds out in a spiral pushing the oldest seeds out to the edge. This could go on
indefinitely with new seeds constantly being produced and pushing out the older ones in a
spiral formation. The spirals themselves are interesting, if you start counting the the sunflower
seeds that are spiraling outwards in a clockwise direction in Figure 6 you should get 89 spirals at
the edge in one direction and 55 spirals in the other direction at the edge again both numbers
fall into the Fibonacci sequence. The same spiral sequence also appears in pine cones. If you
look at Figure 7 and 8 you can see and count the spirals going in both directions.
Figure 6:

Figure 7:
Phyllotaxis is the arrangement of leaves on a team and in relation to one another [Mer].
Figure 8 shows how the leaves pattern of growth. The leaves grown in a pattern so that a leaf
above doesn’t hide the leaf below so each leaf gets adequate sunshine and water. The starting
leaf is marked with an X in figure 8. Notice how in Figure 8 the third and fifth leaf are both
under the starting leaf. They are not centered under the starting leaf but some part of the leaf is
under the starting leaf staring a new spiral. If you look closely you will see that the eighth leave
is directly under the starting leaf. Notice that each leaf under the starting leaf is a Fibonacci
number.
The leaves under the starting leaf are not the only way you see the Fibonacci sequence
in this particular plant. By looking down from the top of the same plant we looked at in Figure 8

we can see the Fibonacci sequence appear in spirals looking down from the top. There are five
clockwise rotations passing 8 leaves there are also only 3 rotations in the anti-clockwise
direction. The Fibonacci sequence appears in many places in nature. The spirals on the pine
cone discussed also appear on pineapples, cauliflower, and even Romanesque Broccoli has
beautiful spiral patters that also have numbers in the Fibonacci sequence.
Figure 8:
Figure 9:

Fibonacci and golden ratio in popular culture
The Fibonacci sequence and the golden ratio have made their way into pop culture. The
Fibonacci sequence has shown up in comic strips, television shows, books and movies. One
popular book and movie that the Fibonacci sequence shows up in is the Da Vinci code by Dan
Brown. In Robert Langdon uses the Fibonacci sequence to open a safe and the sequence is

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- Winter '15
- Andrew Martino
- The Da Vinci Code, Golden ratio, golden rectangle