roughly proportionate divisions,
they are also considered a fractal.
Courtesy image/Mitchell Newberry
But a University of
Michigan researcher noticed that this power law does not fit
And they may revise when
to expect the next Big One.
That's because people can have any amount of money in their bank accounts.
That's not exactly the case with events such as earthquakes because of how they are recorded on the Richter scale.
The Richter magnitude of earthquakes increases or decreases in increments of 0.1, exponentially. A magnitude 3.1 earthquake is 1.26 times as powerful as magnitude 3.0 earthquakes, so not every value is possible on the scale.
Richter scale is an example of a
concept called "self-similarity,"
or when an event or thing is made of proportionately smaller copies
So, to account for events that change in exact proportions, Newberry and his co-author Van Savage of the University of California, Los Angeles, constructed the discrete power law.
infinitely repeats itself,
Wikimedia user Leofun01
In earthquakes, that exponent, called the Gutenberg-Richter 'b value,' was first measured in 1944 and indicates how often an earthquake of a certain strength is likely to occur.
Newberry's discrete power law produced an 11.7% correction over estimates based on the continuous power law, bringing the exponent closer in line with the historical frequency of big earthquakes.
Even a 5% correction translates to a more than twofold difference in when to expect the next giant earthquake.
Newberry noticed the flaw in the continuous power law in his study of the physics of the circulatory system.
The circulatory system begins with one large blood vessel:
As the aorta splits into
different branches - the carotid and subclavian arteries - each new
branch decreases in diameter by roughly two-thirds.
It indicated that a blood vessel might be only slightly smaller than the trunk from which it branched instead of around two-thirds of that trunk's size.
So Newberry reverse-engineered the power law...
By looking at blood vessels, Newberry could deduce the power law exponent from two constants:
Measuring vessel sizes at every division, Newberry was able to solve for the distribution of the blood vessels.
Newberry's study (Self-Similar
Processes Follow a Power Law in Discrete Logarithmic Space)
is published in the journal Physical Review Letters.