A fractal is an infinitely recursive (self-repeating) pattern. Through repetitive scaling, simplicity leads to seeming complexity. Fractals aren't truly complex because the same information can be used to describe each scope of the pattern.
Obvious fractals are abundant in nature, in the forms of trees, mountains, rivers, hurricanes, galaxies, and more. Here are some examples:
Fractals are common enough appearances in nature that art using fractals can easily appear more realistic:
Because the flower inspired me, I tried making a couple of my own:
I also generate many realistic nebulae for my spacescapes using fractal patterns:
Procedural generation based on fractals is extremely powerful, allowing for realistic world generation in simulations and games:
I expect that the universe is a fractal. Both the universe and fractals are infinite, sizeless, and relative. Size doesn't apply to infinity, because infinity is all-encompassing. Relativity does, however. A zoomed-in aspect of a fractal is relatively smaller compared to a more zoomed-out scope. The universe is definitely relative, too... difference/relativity is necessary for change and experience.
At vastly different scales, the structure of neurons and the structure of the universe look remarkably similar..
We're all familiar with waves at the beach..
More fundamental, mathematical waves are pretty recognizable as well..
Many things point to the idea that the universe is inherently wavelike:
• Think about vibration... it is a rhythmic jiggle. All vibration is wavelike. All change is motion, and motion can appear really wavelike. The vibration of the hypothesized quantum strings of string theory would be waves, meaning the universe is composed entirely of vibrating waves..
I propose that waves and fractals are one and the same manifestation, the essential form of the universe.
Think about it... both fractals and waves are infinite, sizeless, and relative. These are the key properties of the universe as well. Fractals are nature's elegant method of achieving apparent complexity through actual simplicity. Waves are nature's way of exhibiting difference, of changing constantly. What would a fractal wave be like? It would be infinitely wiggled, in an elegantly simple way. Yet it would also be seemingly complex from a relativity-allowing perspective like that of one's personal senses. Senses, then, make up our entire experience, and they are described embodied solely as vibration. Mountains we perceive, for example, would be a wiggle within the fractal wiggle of rocky formations. Branches are the wiggles within the fractal wiggles of trees. And so as well for each other aspect in existence, in infinite/universal continuity.
There is mathematical evidence behind the fractality of waves, too. The slope of a sine wave is a cosine wave, and versa. That means that no matter how many times you find the derivative of a waveform, it is another waveform; the pattern is fractal because its rate of change is reminiscent of its change; there is meta similarilty.
I think the following comparison provides an excellent insight into why humans have tended to perceive the universe discretely. While in reality the essence of the universe is a waveform..
...we are still at a stage where we perceive these waveforms merely as binary crest\trough dots, like so..
In reality, each identifiable thing is smoothly connected. Furthermore, this one wave is a fractal waveform because there are wiggles within wiggles. That is your experience of the universe. You can understand this from any of the following equivalent perspectives:
0 - there is no "individual" waveform as individuality is just recognition in one's mind; there is just the universe
1 - there is only the single waveform, the universal wave, and our sensory experience is its flow
∞ - the waveform of the universe is infinitely fractally divisible into each of the universe's identifiable aspects
You can really see (since this example is so holistic / zoomed out from any arbitrary locality) how a discrete explanation (as opposed to a fundamental indiscrete equivalency explanation), like one using the number 7, would be way too arbitrary to describe the essence of the universe. The universe can best be described, by totally applicable explanations, as something akin to a fractal wave. What would a fractal wave look like? You have only to look around you, at the universe (yourself).