Graphing one of these objects versus scale on a log-log plot yields a straight line with the slope equalling this object's namesake dimension. A related quantity that characterizes these objects is the topological dimension, which is always smaller than the Hausdorff dimension. In addition to space-filling curves and Julia sets, the most famous example of these objects is named for a mathematician who studied the coastline of Britain. They include the Sierpinski gasket, the Koch snowflake, and the Mandelbrot set. For 10 points, name these self-similar patterns that, at every scale, contain smaller copies of themselves
Graphing one of these objects versus scale on a log-log plot yields a straight line with the slope equalling this object's namesake dimension. A related quantity that characterizes these objects is the topological dimension, which is always smaller than the Hausdorff dimension. In addition to space-filling curves and Julia sets, the most famous example of these objects is named for a mathematician who studied the coastline of Britain. They include the Sierpinski gasket, the Koch snowflake, and the Mandelbrot set. For 10 points, name these self-similar patterns that, at every scale, contain smaller copies of themselves.
Graphing one of these objects versus scale on a log-log plot yields a straight line with the slope equalling this object's namesake dimension.
{fractal}s