self-similarity

Self-similarity is a key characteristic of fractals, a class of complex geometric shapes distinct from traditional Euclidean geometry. These shapes often have a "fractional dimension" and are used to describe irregular natural phenomena like coastlines and mountain ranges.1

The term "fractal" was coined by Benoit B. Mandelbrot and is derived from the Latin word for "fragmented". Many fractals exhibit self-similarity, meaning their component parts resemble the whole object. This pattern repeats at smaller scales, and in abstract fractals, it can continue indefinitely. This property means the object remains unchanged when scaled larger or smaller, a concept known as scaling symmetry.12

An example is the snowflake curve, where each part is a scaled-down version of the whole, repeating infinitely. This self-similarity contributes to a fractal's complexity, often indicated by its non-integer fractal dimension.1