- Branching Pattern in Trees: When the main trunk of a tree branches out, it gives rise to a side-branch, which will further go on to divide and produce two more branches, form two new growth points. This occurs at each branching event along its lifetime, whose number follows the Fibonacci progression and the ratio of new branches to old is 1.618 at each branching node.
- Spiral Galaxies: The Fibonaccian spiral is also observed in the case of a spiral galaxy. Certain other entities within the galaxy also exhibit the golden ratio, such as the ratio of the diameters of Saturn and its rings; the ratio of the distances of Venus and the Earth from the Sun;....

Various features of the human face exhibit the divine proportion. It is seen when one compares the relative position of facial features. Some common examples of such ratios are:
+ Center of the pupil - Bottom of the teeth - Bottom of the chin
+ Outer and inner edge of the eye - Center of the nose
+ Outer edges of the lips - Upper ridges of the lips
+ Width of the center tooth - Width of the second tooth
+ Width of the eye - Width of the iris
Along with these, the human face also shows the golden ratio in terms of vertical and horizontal ratios. In addition, the shape of the ear resembles the shape of a Fibonaccian spiral. Numerous studies have concluded that faces with facial features that exhibit a precise golden ratio are deemed to be highly attractive and regarded as extremely beautiful.
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DNA

A DNA molecule is 34Å in length and 21Å in width. The ratio is approximately equal to the golden ratio. The same is true for the ratio of the two grooves of the helical DNA molecule, i.e., the major (21Å) and the minor (13Å) groove.
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Mona-Risa by Leonardo Da Vinci

This picture includes lots of Golden Rectangles. In above figure, we can draw a rectangle whose base extends from the woman's right wrist to her left elbow and extend the rectangle vertically until it reaches the very top of her head. Then we will have a golden rectangle.
Also, if we draw squares inside this Golden Rectangle, we will discover that the edges of these new squares come to all the important focal points of the woman: her chin, her eye, her nose, and the upturned corner of her mysterious mouth.
It is believed that Leonardo, as a mathematician tried to incorporate of mathematics into art. This painting seems to be made purposefully line up with golden rectangle.

2. Seed heads
The head of a flower is also subject to Fibonaccian processes. Typically, seeds are produced at the center, and then migrate towards the outside to fill all the space. Sunflowers provide a great example of these spiraling patterns.
In some cases, the seed heads are so tightly packed that total number can get quite high — as many as 144 or more. And when counting these spirals, the total tends to match a Fibonacci number. Interestingly, a highly irrational number is required to optimize filling (namely one that will not be well represented by a fraction). Phi fits the bill rather nicely.

3. Pinecones
Similarly, the seed pods on a pinecone are arranged in a spiral pattern. Each cone consists of a pair of spirals, each one spiraling upwards in opposing directions. The number of steps will almost always match a pair of consecutive Fibonacci numbers. For example, a 3-5 cone is a cone which meets at the back after three steps along the left spiral, and five steps along the right.