Planet Earth does not see mixed prints as a fashion faux pas - in fact, she wears them quite well. Take a look around and notice all the patterns nature throws at us - the path of a river, the shape of a cloud, ripples in sand, stripes on a zebra, the growth pattern of a plant - each of these things is more than random. They are natural patterns, fully explained by math, physics and biology, and they can be no other way.
Everything that grows has some kind of symmetry. Animals tend to have bilateral symmetry because they move in one direction - having two sides with identical parts helps with locomotion. That's not to say it's necessary, though - starfish have five-fold symmetry, but each of those five lobes has bilateral symmetry.
Some plants have bilateral symmetry as well, but most have radial symmetry - so do some animals, like sea anemones. Radial symmetry is less suited to locomotion (could you imagine trying to walk in a straight line if you were shaped like a daisy?), so it is usually found in stationary life.
Ripples happen when wind acts on a solid or liquid surface - the ripples in the sand on the beach are very similar to the waves in the ocean, just in different mediums.
Picture a desert: the wind blows the sand into a crescent shape, with the curve receiving the brunt of the wind. The longer the wind blows, the more sand piles up, but only a little bit at a time. Because the dune is built at such a gradual pace, it is able to reach very unstable proportions without falling down, but eventually comes the grain that breaks the dune. When steepness of the outside the curve exceeds the steepness of the inside, an avalanche happens and a new pattern is formed.
Look at a nautilus shell, a snail, a head of lettuce, or a Bighorn sheep.
Look at the spiral - how does it just spontaneously form in such a perfect curve? It takes both math and science to fully explain, but the proportions of the spiral can be predicted using Fibonacci series - a series of numbers in which each number represents the sum of the two previous numbers - for example, 1,1, 2, 3, 5, 8,... etc. Spirals happen spontaneously because natural systems don't like to waste energy. Out of all possible forms, the one that will arise naturally is the one that uses the least amount of energy. Since each layer in a spiral lends support and structure to the one above, spirals are a very low-energy form.
You've seen fractal art before, right? Google it. They're images (computer-generated) in which each individual unit is so similar to the overall shape that it is impossible to tell whether you're zoomed in or out. Nature does fractals everywhere.
Fractals are great at branching - they're in trees, snowflakes, fault lines, mountains, even your own circulatory system. They're not as precise as computer-generated images because nature doesn't do perfect, so natural fractals are only good up to four levels or so. But the branching trait is so vital to life that without it, our planet would be a barren rock.
Animal spot/stripe colorations are a puzzle. We know why they have them - they serve as camouflage, or warning, or a mating signal. We know how they get them, sort of - the patterns arise according to the rules of math and physics that govern all pattern formation, and certain pattern variations are favored in evolution.
But we still don't know exactly how each animal ends up with its particular variation. It's thought that certain chemical signal cells can trigger the skin or hair to grow a different color than the surrounding area. If there are many, many of these cells all over, the skin will be a uniform color. If there are only little clusters of these cells, only certain sections of the skin will turn colors and become stripes or spots.
Nobody does patterns like nature, and there's a concrete explanation behind every single one. Nature has always been the envy of artists and an enigma to scientists - she is, in short, the perfect companion.