I see this from a different perspective. I am not assigning purpose to the universe and I am absolutely convinced that it is moving toward symmetry. All of science speaks of these fundamental constants that bring order to the chaos.
It is the universal constants that record the occurrence of regularly recurring patterns, and the evolution of complex universal mathematics.
I don’t think purpose makes any difference, except that purpose (motive, intent) requires understanding, and lack of understanding may lead to incorrect actions, whereas the universe makes no mistakes. It has no purpose other than to act mathematically when presented with a differential equation in a dynamic environment.
Symmetry in nature is all around us. If it isn’t, it is in process of creating or regaining symmetry. And it is not by accident, it’s mathematical.
The Fibonacci sequence in nature is an evolved equation for balancing vertical growth.
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https://www.researchgate.net/figure/Spiral-symmetry-in-nature-6_fig4_237838275
And then spacetime itself may be fractal, as an expression of ultimate symmetry via self-similarity.
We commonly recognize when shapes demonstrate symmetry under the three familiar transformations of reflection, rotation, and translation. Fractals demonstrate a fourth type of symmetry ; they possess “self-similarity.” Self-similar objects appear the same under magnification.
Familiar Symmetries
Scaling Symmetry
http://www.brotherstechnology.com/docs/fractals.pdf
Fractal geometry is also common in chemistry. The phenomenon is expertly demonstrated by copper crystals, which branch out in all directions like tree limbs. Each “twig” is a new growth point—as it branches out, it develops into solid metallic copper. Because of their arborescent nature and unique reddish-brown color, copper crystals are often grown for art.
Note that in a dynamic environment perfect symmetry is impossible, but always an approximation. Hence the term “tolerance”.
It is the acceptable deviance from perfection and dependent on the physical properties of the interacting values.
What is Tolerance?
In terms of measurement, the difference between the maximum and minimum dimensions of permissible errors is called the “tolerance.” The allowable range of errors prescribed by law, such as with industrial standards, can also be referred to as tolerance.
It is clear that in a physical world, symmetry is the most efficient way to express mathematical patterns, such as mirror images.
Introduction
Many geometric concepts like lines
A line is a set of infinitely many points that extend forever in both directions. Lines are always straight and have no width.
A mathematical object.
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or polygons
A polygon is geometric shape that is made up of straight line segments. Polygons cannot contain any curved sides, or holes. For example, a square is a polygon but a circle is not.
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Polygons were “invented” by mathematicians.
Symmetry, on the other hand, is everywhere around us. Almost all plants, animals, and even we humans are symmetric.