McLean's Nuggets

摘要

When each piece of a shape is geometrically similar to the whole, both the shape and the cascade that generate it are called self-similar. -BB Mandelbrot, The Fractal Geometry of Nature, 1982. For newcomers to the field of fractals and fractal geometry, we may introduce the fractal as a term to describe self-similarity. Useful examples in the natural world include the fern, which if you remove a stem looks remarkably 'similar' to the leaf from which it was removed, or the more edible broccoli and cauliflower, which exhibit at least three scales of 'similar' morphology - break off a broccoli floret and you have a broccoli in miniature, etc. Another well-used example is the profile of a coastline, which when studied in plan through aerial photography or mapping exhibits a similar geometric profile at a range of scales.