Types of Fractals
Peano curves is a name given to any fractal whose fractal dimension is 2. This means that a Peano curve is not merely a curve, but a curve that became so twisted that it became 2-dimensional and actually occupies some area on a plane. The most famous representative, after which this type of fractals was called, is the Peano Curve. It is a base-motif fractal with a line segment for a base and a very simple motif:
The final image of this fractal is a square, or in other words, it "fills" a square. Other Peano curves, such as the Cesaro’s and Polya’s sweeps fill figures like triangles. Sometimes, a Peano curve fills a figure that is itself a fractal. An example is the Snowflake Sweep, which fills the Koch Snowflake:
Another example is the Dragon Fractal, whose outer shape is also a base-motif fractal:
Note that this fractal is a representative of paper-folding fractals, all of which are, indeed, Peano curves. The other ones, though, usually create more regular shapes, such as triangles..