A fractal is a shape that contains copies of itself on smaller and smaller scales. You can find fractals everywhere in nature. Part of a fern looks like the fern as a whole:
Fern as fractal (source)
Part of a tree looks like the tree as a whole:
Tree as fractal (source)
Part of a landscape looks like the landscape as a whole:
Landscape as fractal (source)
You can also create fractals for yourself. Here are three that I’ve constructed:
Fractal #1
Fractal #2
Fractal #3 — the T-square fractal
The three fractals look very different and, in one sense, that’s exactly what they are. But in another sense, they’re the same fractal. Each can morph into the other two:
Fractal #1 → fractal #2 → fractal #3 (animated)
Here are two more fractals taken en route from fractal #2 to fractal #3, as it were:
Fractal #4
Fractal #5
To understand how the fractals belong together, you have to see what might be called the scaffolding. The construction of fractal #3 is the easiest to understand. First you put up the scaffolding, then you take it away and leave the final fractal:
Fractal #3, scaffolding stage 1
Fractal #3, stage 2
Fractal #3, stage 3
Fractal #3, stage 4
Fractal #3, stage 5
Fractal #3, stage 6
Fractal #3, stage 7
Fractal #3, stage 8
Fractal #3, stage 9
Fractal #3, stage 10
Fractal #3 (scaffolding removed)
Construction of fractal #3 (animated)
Now here’s the construction of fractal #1:
Fractal #1, stage 1
Fractal #1, stage 2
Fractal #1, stage 3
↓
Construction of fractal #1 (animated)
Fractal #1 (static)
And the constructions of fractals #2, #4 and #5:
Fractal #2, stage 1
Fractal #2, stage 2
Fractal #2, stage 3
↓
Fractal #2 (animated)
Fractal #2 (static)
Fractal #4, stage 1
Fractal #4, stage 2
Fractal #4, stage 3
↓
Fractal #4 (animated)
Fractal #4 (static)
Fractal #5, stage 1
Fractal #5, stage 2
Fractal #5, stage 3
↓
Fractal #5 (animated)
Fractal #5
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