That example is the (*) "strange attractor".
One mathematician defined these objects as all objects whose Hausdorff dimension is greater than their topological dimension, and that mathematician's namesake "tree" is an example of one of these. Many of these objects can be expressed in terms of Lindenmayer systems, and one example of these can be found on a Henon map, and is used to determine a system's trajectories. That example is the (*) "strange attractor". Space-filling ones, such as the Hilbert curve, do not satisfy the above definition given by Mandelbrot and other ones, such as the Rabbit and Dendrite types of these objects, can be generated using Julia sets. Including the real-life examples of coastlines and snowflakes, FTP, name these mathematical objects who portray a degree of self-similarity at all levels of magnification.
One mathematician defined these objects as all objects whose Hausdorff dimension is greater than their topological dimension, and that mathematician's namesake "tree" is an example of one of these.
{fractals}