On Friday, September 14, 2012 16:22:07 Metric Rules Info wrote: > Thank you so much for responding! I am not a unit expert; therefore, please > forgive me if my understands are incorrect. > > > > What would a 3-D model of a metric cube, going from very small to very large > look like? And would not other aspects of the cube (like length, water > mass) also have a consistent, repeating pattern? I assume that SI units are > infinite? Are all units interrelated or just some? > > > > According to the Fractal Foundation website: A fractal is a never-ending > pattern. Fractals are infinitely complex patterns that are self-similar > across different scales. They are created by repeating a simple process over > and over in an ongoing feedback loop. Driven by recursion, fractals are > images of dynamic systems - the pictures of Chaos. Geometrically, they > exist in between our familiar dimensions. Fractal patterns are extremely > familiar, since nature is full of fractals. For instance: trees, rivers, > coastlines, mountains, clouds, seashells, hurricanes, etc. Abstract > fractals - such as the Mandelbrot Set - can be generated by a computer > calculating a simple equation over and over. > > > > I am not certain about this relationship but I consider it quite interesting > to think about. If it were correct, it could change the conversation about > metric units.
A fractal is something whose Hausdorff dimension exceeds its topological dimension. You can have a coastline which is 100 km long if you measure it at the kilometer scale, 110 km long at the hectometer scale, 133.1 km long at the meter scale, and 177.1561 km at the millimeter scale. That's a fractal. The meter stick you measure it with is a straight line segment, not a fractal. If you measure a meter stick in micrometers, it is still a meter long. The fractality of the coastline when measured in the metric system is in the coastline, not in the metric system. Pierre -- lo ponse be lo mruli po'o cu ga'ezga roda lo ka dinko
