A change can be of many different kinds, but the one we’re particularly interested in is the change that is fractal.
Fractal change is intriguing because it is prevalent in nature. The most adaptive, resilient processes in life—from our heartbeat, breathing, and movement to the coastal and plant growth patterns and galaxy distributions—are fractal in nature.
Studying fractal change can therefore help us grasp—or at the very least, attune ourselves to—the fundamental principles of nature.
What is a fractal change?
Let’s assume what we know about fractals: they are self-similar structures that repeat across different scales.
It’s easy to imagine them visually. A fractal follows a very simple principle: apply the same type of change at different scales; the bigger the scale, the bigger the change. As a result, complex, beautiful structures emerge.
If a fractal exists in space, it also exists in time.
In fact, if we talk about change, we have to be talking about time.
So what is a fractal in time?
If we use the same definition as before, it is a pattern of change that repeats across different scales.
Let’s take the smallest scale of 4 seconds and imagine there is only one type of change: between the slow (0) and the fast (1), or silence (0) and a beat (1). We will experience something like this:
0 0 1 0
translating into
slow – slow – fast – slow (a gust of strong wind during calm weather)
or
silence – silence – beat – silence (a perturbation in a period of silence)
If we observe this same process for 2x longer (8 seconds), we will experience that acceleration (or impulse) twice:
0 0 1 0 1 0 0 0
slow – slow – fast – slow – fast – slow – slow – slow (two gusts of wind during calm weather)
or
silence – silence – beat – silence – beat – silence – silence – silence (two perturbations in a period of silence)
Then we increase the observation period by another 2x (16 seconds), and we experience this same change re-emerging on a bigger scale, for a longer period of time:
0 0 1 0 1 0 0 0 0 0 0 1 1 1 1 0
two smaller gusts and one longer gust of wind during calm weather
or
two perturbations in silence followed by a period of strong perturbation
Therefore, if the principle is to induce a perturbation, its nature will be fractal when the longer we observe it, the stronger the principle is expressed.
We can also see that certain states emerge.
(You can verify that this is a fractal state by using the online open-source DFA calculator that will compute the alpha component for this sequence at fractality.app)
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Another version of this dynamic is when we push variability between the individual beats towards a more fractal state:
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Some thoughts so far:
These states do not last for a very long time; they shift one into the other. Nothing is allowed to go on forever, but everything is allowed to go on for some time. (With some breaks in between).
A slow state will contain a fast state. A fast state will contain a slow state. Like yin and yang.
The process seems to have memory (a previous iteration will likely affect the next iteration) and change tends to happen in bursts of activity.
Observing a state for a short time will reveal a similar pattern as a longer observation. However, the longer the observation, the more prominent the states become. Whether we zoom in or zoom out we ecounter the same principle operating at different scales….
The system exhibits non-equilibrium stability.
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Compare this pattern to a random sequence of 1s and 0s generated by a machine:
0,1,0,1,0,1,1,0,0,1,1,1,0,1,0,0
Here it’s a 50% chance of 1 and 0. The change is random. There is no memory in the system; therefore, states don’t really have time to form. The system seems unstable, as there are no specific states that depend on the scale of observation. Patterns emerge only when we put the system on a loop.
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The fractal change we are talking about here is omnipresent in living systems.
Heart rate variability (HRV) and breathing exhibit fractal dynamics when our system is in its most adaptive, resilient state.
Neuronal firing patterns are also fractal in nature.
Human gait and involuntary movement in a calm, relaxed, adaptive state will exhibit fractal properties.
Many natural processes, such as cloud formations, rain drops, coastal formations also form fractal patterns.
If we tune our system to this dynamics, we can entrain ourselves to be aligned with the fundamental rhythm of nature which is adaptive and healthy at its core.
We can achieve this in several ways.
One direct way is through sound.
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Another way is through using haptic feedback and creating a biofeedback loop with a fractal metronome. One can then adjust their breathing accordingly to the rhythm, which will entrain the body to the natural fractal dynamics and will, in turn, make their HRV (heart rate variability) more fractal. This will generate a more resilient, adaptive state. Here is an example of a rhythm like this made with the SomaSync app: