One of the conclusions of fractal
geometry is a fact that fractals unlike traditional Euclidean shapes
lack characteristic scale. Those "fractured" objects are self-similar -
defining geometry is clearly visible on multitude of scales. It is known
that self-similarity is observed not only in formally defined geometric
objects, such as Sierpinski
triangle
or Koch
snowflake,
but also in the surrounding nature. One of my most favorite examples is
a comparison of tree, its branches and a leaf (for more inspiring
examples see introduction of Fractals
section)
- they all have branching structure and something green filling the
extra space in between.

The interesting thing, in context of the topic in focus, is that one can
extend fractal formalism beyond formal or natural geometric shapes. It
is also noticed that some of the natural processes exhibit fractal
features in their time series! It is known that geoelectrical processes
[1], heartbeat [2]
and even human gait [3] time series posses
this feature. While financial market, frequently analyzed on Physics of
Risk website, time series are also no exception [4, 5]. Though the aforementioned
time series are much more complex - they exhibit not monofractality
(single manner self-similar behavior as the aforementioned formal
geometric fractals do), but multifractality!