Self-similarity and periodic processes in the nature.

Periodic processes on Earth, such as day-night cycle (period - 86400 seconds), the time of year (an annual cycle) are responsible for the self-similar forms of shores of seas, rivers, forms of mountains. The mechanism of periodic processes and difference in structure of the earth and air led to a self-similar (fractal) form of trees and respiratory ways in a human body. Everywhere, where the effective exchange between the firm and liquid or gaseous environment in the presence of periodic processes is required, gradually during evolution self-similar structures are formed. Periodic processes in an organism of animals and the person such as heartbeat and a breath cycle (the period ~ 1 second) created in a body, and in particular in a brain self-similar structures responsible for an effective exchange of substance, energy, and finally (at thinner level) - information. The ingenious guess of ancient hunters of truth consisted in awareness of importance of periodic processes in the nature. Periodic process of meditation * on the mantra or prayer, having a period close to the periods of breath and heartbeat, is the organizing principle of the inner wheel of time in the Kalachakra Tantra and leads to harmonization, alignment mind, body and nature.


Periodic processes in the nature or an external wheel of time in Kalachakra tantra.

Long-period oscillations of the eccentricity of the orbit of the Earth.
93000 years

The river basin of Amazon, connects the Andes and jungle of Amazonia with the Atlantic Ocean and has self-similar fractal structure.

Long-period oscillations of the angle of inclination of the Earth's axis to the plane of its orbit (nutation)
41000 years
Turning the earth's axis (precession)
25750 years
Solar Activity
11 - 17 years
Awakening of cicadas
Rotation of the Earth around the Sun
year = 365 days
fractal tree

Self-similar form of the tree is optimal in the interaction of the earth and air.

Rotation of the Moon around the Earth

lunar month

29 days

Earth rotation round an axis

day 86400 seconds

Dream and wakefulness cycle
5 seconds
Lungs and bronchi
Fractal form of the bronchi.
1 second
The circulatory system of the human
Self-similar structure of blood vessels.

Meditation on breath

or mantra **

1 - 5 seconds
Mental process


* - Thinking. Thinking on a certain subject. In thinking on a particular topic we make a start from a certain initial thought. Let's call it initial thought. Then the thought process would be that we once again starting from the initial thought on a specific topic will come to some new ideas. Then we will think on the same topic starting from this (new) thought. The result of this thinking is (super) new idea. And so on.

What can be considered the end of reflection on a specific topic?

1. Satisfactory completion reflections - the achievement of steady state results, the attractor (attract, draw) in the space of meaning.

2. Unsatisfactory ending thinking - this is when we, in our thinking, more and more moving away from the topic, switch to another topic under the influence of some uncontrollable external or internal causes. If we feel that not enough thought on a given subject (attractor is not reached in one form or another - a point of attraction or trajectory in the simplest case), then say "we moved away from the topic", and "where we left off?".

The essence of the model lies in the fact that we compare the process of thinking and iterative process:

z[1] = F( z[0] ),
z[2] = F( z[1] ),
. . .
z[i+1] = F( z[i] ),
. . .
where z [0]-the original or initial idea F (z) is a transformation function.


** - conscious process, as opposed to breathing and heartbeating, for more details see the review article about the kinds of meditation.


© 1992 - 2014 Alexander Kucherenko


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