This is a special guest blog article by Jiyeong Kim, a 3rd year PhD student in Computational Physics Laboratory at Tampere University in Tampere, Finland. Her research topics are time-series analysis and nonlinear dynamics in biological and financial systems. She can be reached at jiyeong.kim@tuni.fi.
When you think of the word fractal, you probably have
certain images immediately coming to your mind: infinitely continuing patterns
and swirls! I find them fascinating and quite beautiful, especially when they
are created in nature. Common examples of fractals in nature are snowflakes,
tree branches, and Romanesco broccoli. Now, these are geometric fractals,
but the concept of fractals is not limited to geometry.
 |
| Romanesco
broccoli. Photo by Aurelien Guichard Flickr: Borough Market |
The definition of a fractal is a structure that displays
self-similar patterns across different scales. For geometric fractals, the
scale is spatial one, but the scale can also be time. Temporal fractals
are fluctuations that are statistically similar over multiple time scale; that
is, when you look at a fractal signal at different scales, whether it’s 3
minutes, 30 minutes, or 3 hours, the fluctuations are similar. This type of
signals are also known as 1/f noise, or pink noise.
What’s really fascinating about the 1/f noise is that it
appears in many biological systems, including us humans, and it also seems to
play an important role in our health. The most famous example of 1/f noise is
our heartbeat. Even though many people believe that our heart rate should be
regular (apart from it changing due to activities such as exercise or sleep), this
is far from the truth.
Take a look at the figure below. Can you guess which one
belongs to a healthy person?
 |
Which one belongs to a healthy person?
Image: Goldberger et al., PNAS February 19, 2002 99 (suppl 1) 2466-2472 |
The correct answer is B! If you got it right, I am very
impressed. When we showed these graphs to a group of cardiologists, not everyone got it
right either. A and C belong to patients with several congestive heart failure syndromes,
and D to a patient with atrial fibrillation.
So our heart rate, it turns out, fluctuates in a very complex manner that is neither too regular nor too random--it’s fractal! Having a fractal structure is often related to the system’s robustness against external stress; that is, our heart can adjust to sudden changes better in the presence of fractal dynamics. Many scientists have confirmed the presence of fractality and its alteration due to aging and heart diseases. Though fractal analysis is not used yet in clinical practices, it has a great potential as a noninvasive diagnostic tool. Who knows? All the handy heart monitoring devices out there may soon add a feature that tells you how fractal your heart rate is!
So our heart rate, it turns out, fluctuates in a very complex manner that is neither too regular nor too random--it’s fractal! Having a fractal structure is often related to the system’s robustness against external stress; that is, our heart can adjust to sudden changes better in the presence of fractal dynamics. Many scientists have confirmed the presence of fractality and its alteration due to aging and heart diseases. Though fractal analysis is not used yet in clinical practices, it has a great potential as a noninvasive diagnostic tool. Who knows? All the handy heart monitoring devices out there may soon add a feature that tells you how fractal your heart rate is!
Heartbeat is not the only thing that is fractal within us.
Respiration rate, blood pressure, gait (stride-to-stride fluctuation), glucose
level, gene expression, DNA sequences...the list goes on. One I find
especially interesting is finger tapping.
When you tap your finger to a certain tempo, you can imagine
that it won’t be perfect like a metronome. Its deviations from the intended
beats (the metronome) have fractal structure. A similar phenomenon also occurs in
drumming. When a drummer performs, no matter how hard he/she tries, there are
always some deviations from the exact beat, which turn out to be also fractal.
The importance of the fractal deviations in drumming was revealed in a survey.
Between two humanized drumming samples, one with Gaussian fluctuations
and the other with 1/f fluctuations, many preferred the latter. In other words,
the presence of 1/f fluctuations makes music sound more human.
A recent study conducted with a real-world data analyzed the
song I Keep Forgettin’ (1982) by Michael McDonald.
The drummer in the song is Jeff Porcaro (1954-1992), who was a session musician
behind many recordings of, e.g., Michael Jackson and Madonna, and a member of
major rock bands Steely Dan and Toto. The song features Porcaro’s well-known
single-handed hi-hat technique that is particularly smooth and groovy; it’s the
really fast, high-pitched beats in the background, if you are listening to the
song. Guess what they found? 1/f fluctuations in both intervals and amplitude.
The study implies that behind the groovy feel of a good drummer is the
naturally occurring fractal fluctuations in the rhythm.
What you also need to know is that the 16th notes Porcaro
plays is about 150 ms apart, and deviation is only about 20 ms. That is, there
should be no way that we can detect the deviations with our ears. But somehow
we can tell from the groovy feel that something is there. So the ‘groove’ is
somehow also related to how we perceive the timing and rhythm. Could it be
related to the fact that the nerve spike intervals have fractal fluctuations?
We continue to discover fascinating fractal phenomena and
there are still many questions to be answered. Many researchers are working
towards unlocking the secrets of fractal dynamics in human body, in nature
(temperature, precipitation, ozone level, climate dynamics), and in our society
(internet traffic, highway traffic, stock market dynamics, they all exhibit
fractal fluctuations!). One of the biggest question in the studies of fractal
time series is certainly the origin of fractality. Recent studies, including my
own, have shown that we can find fractal dynamics even at the cellular level;
clusters of heart cells, grown from stem cells in laboratory, beat together spontaneously
exhibiting fractal-like fluctuations in their beat rates without any neural
input. Looks like we are full of fractals all the way down to our cells!
Sources:
No comments:
Post a Comment