These objects exhibit self-similarity on very small scales, and resemble natural features like coastline and snowflakes.
The Hausdorff dimensions of these objects are greater than their topological dimensions. Examples of these objects include the Menger sponge and the Sierpinski triangle, and types of them, such as the Cantor set, can be created by infinitely iterating a recursive equation. These objects exhibit self-similarity on very small scales, and resemble natural features like coastline and snowflakes. For 10 points, identify these geometric spaces named by Benoît Mandelbrot, which contain infinitely smaller copies of themselves.
The Hausdorff dimensions of these objects are greater than their topological dimensions.
fractals