Fibonacci pattern (top): Sun flower, Pineapple
Logarithmic spiral (bottom): Milkyway galaxy, Nautilus shell
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 ..... did you notice anything? Exactly, each number (after the initial 0 and 1) is the sum of the previous two. The Fibonacci sequence is interesting and will find its recurrence in nature. For instance, a lot of common flowers have 1, 3, 5, 8, 13, or 21 petals. Sunflowers, for instance, have 34, 55, or 89 petals. The study of pineapple will indicate that the row of scales on its surface follow two spirals sloping in the opposite directions. Now, if you count the number of scales along the spirals, the numbers exhibit Fibonacci pattern like (8 and 13) with 8 spiraling along the right and 13 to the left.
Spiral is another interesting phenomenon. The logarithmic spiral (angle between the tangent and the radius of the vector is same for all points of the spiral) often appears in nature: Milkyway galaxy, nautilus shell, pine cones, deer antlers, broccoli, human fingerprints, etc. The logarithmic spiral is also remarkable owing to its self-similarity. In other words, after scaling (uniformly increasing or decreasing the size), the spirals can be rotated such that they match the original figure. A Mandelbrot set is a great example of the concept of self-similarity.
Deepest part of space to the seed pattern in a sunflower, nature expresses itself in the language of math.