Smaller copies of itself
Zoom into a fern and meet the whole fern again.
A leaflet of a fern
A fern leaf is made of many small leaflets along a stem. Look at just one leaflet.
What does one small leaflet look like?
What this lesson covers
The idea
A fractal is a self-similar shape that contains smaller copies of itself, showing the same or similar pattern over and over again at smaller and smaller scales; fractals occur in nature and in art.
A leaflet of a fern
A fern leaf is made of many small leaflets along a stem. Look at just one leaflet.
What does one small leaflet look like?
- A tiny copy of the whole fern leaf
- A plain straight line
- A circle
Zoom into the fern
Tap a leaflet on the fern, or press a size button. The leaflet is turned upright and enlarged in the second picture. Then try the house too.
The same pattern, again and again
A fractal is a self-similar shape that contains smaller copies of itself, showing the same or similar pattern over and over again at smaller and smaller scales; fractals occur in nature and in art.
The fern has smaller copies of itself as its leaflets, and these have still smaller copies as sub-leaflets. A tree has a trunk, limbs, branches and branchlets in the same way. Clouds, coastlines, mountains and lightning also repeat their pattern.
A house is not a fractal: a window, a door or a roof does not look like a smaller house.
Notes
A fractal is a self-similar shape: it contains smaller copies of itself, the same pattern again at smaller and smaller scales. Fractals occur in nature and in art.
Check yourself
Which of these pictures is a fractal?
A tree has a trunk, limbs, branches and branchlets. Why can a tree be called a fractal?
Every leaf of a fern has 6 leaflets. Every leaflet has 6 sub-leaflets. How many sub-leaflets does one leaf have in all?
Answer: 36 sub-leaflets
6 leaflets × 6 sub-leaflets each = 36 sub-leaflets. At the next smaller size the count grows again.
The tall tower of the Kandariya Mahadev temple at Khajuraho is made up of smaller copies of the whole tower, and those carry even smaller copies. What is this property called?
- A. The house is one plain shape. No part of it looks like a smaller house.
- B. The ball is one plain shape. A piece of it does not look like a smaller ball.
- C — correct. Yes! Every leaflet of the fern is a smaller copy of the whole fern.
- It is tall and green. Size and colour do not decide it. A fractal is about the pattern repeating.
- Each limb or branch looks like a smaller copy of the whole tree — correct. Yes! A branch with its branchlets is a smaller copy of the tree.
- It stands on one trunk. Having a trunk is not enough. A pole has one too, but no part of a pole looks like a smaller pole with branches.
- Mirror symmetry. Symmetry is about matching halves. Here the whole is repeated at smaller sizes.
- Self-similarity — correct. Yes! The shape contains smaller copies of itself.
- Tiling. Tiling covers a flat surface with no gaps. Here a shape repeats inside itself.