Im not sure if randomness is really absence of pattern. Randomness as in chaotic system can have pattern like fractals, but a small change in starting condition will have unpredictible effect on the outcome. In this view randomness is a product of complexity, as number of input factors and relationship between them. Which is why thermodynamics doesnt work in open systems because entropy dominate.
People seem to be confusing two entirely different things
That is, random patterns with repetitive patterns. The former are the characteristic of a random distribution, while the latter of a distribution which is not random. To make things easier to understand and probably to accept, it can be advised to think about the random patterns as irregularities (or grouping). However, if we consider these irregularities at a higher level, their emergence is not random at all
Which of these definitions says about the lack of random patterns?
Its a different definition than chaos theory then.
Unpredictability: Because we can never know all the initial conditions of a complex system in sufficient (i.e. perfect) detail, we cannot hope to predict the ultimate fate of a complex system. Even slight errors in measuring the state of a system will be amplified dramatically, rendering any prediction useless. Since it is impossible to measure the effects of all the butterflies (etc) in the World, accurate long-range weather prediction will always remain impossible. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are images of dynamic systems the pictures of Chaos. Geometrically, they exist in between our familiar dimensions. Fractal patterns are extremely familiar, since nature is full of fractals. For instance: trees, rivers, coastlines, mountains, clouds, seashells, hurricanes, etc.https://fractalfoundation.org/resources/what-is-chaos-theory/Note that snowflakes (as part of fractal patterns) aren't really random. The assumption is that they are simply following their pre-designed or preexisting microscopic structures. I remember they were thought to develop randomly.
Assuming you pour sticky substance on an invisible ball, the substance sticks on the invisible ball and takes its shape. The new shape of the substance could blow the mind of an observe who may even consider it as random.
What make fractal random is that small change in initial condition can lead to a completely different result after a certain number of iterations, so it make them hard to predict.
If you pour the substance many times it will still take the same shape, and the sequence of outcome is still predictible, even if there is no explanation for it, statstics dont require To understand the phenomena to find regularities.
Its interesting to see also why they came up with perlin noise algorithm to give computer generated graphics a more natural look, fractal can be used to generate trees, and adding some perlin noise can change a straight line adding slight twist to it, and can be used to generate 1000 trees that will all look slightly different but still using same core fractal pattern. Even in hair animation they probably use some kind of noise to make it more "realistic".
I Guess its same with Snow flakes that They all Have same core pattern but not two are identical, even if they form in very similar conditions.
Noise is often used to increase the complexity of computer algorithm in a cheap manner, and can end up with result that are statistically close To natural occurrence, even with simple repetitive/ iterative algorithm and very simple primitive patterns.