The way that I came by my element and animal associations is by using the site http://www.turtleluck.com/main-elements/ . I read all the element descriptions: yang wood, yin fire etc. and I read some descriptions of the western sun signs and matched them up according to things they had in common. The air signs were left over, and when I looked at the description of Capricorn it mentioned a 'rarefied air' that is a signature to the sign. That rarefied air means high prestige. The sign is also the mid-heaven, and the heavens is associated with air. Finally, the rooster sign fit Capricorn through the animal's description on turtlelluck.com and through the method that I will describe further down in this post. It makes sense that the bird sign is an air sign. Similarly, it makes sense that the monkey sign is a tree sign in Aquarius! If you look at all the elements when on the circle, you will see that yang signs always oppose yang signs, and yin signs always oppose yin signs.
The animals were tricky. I was lucky enough to have 4 of them in the right position already so that I could discover a pattern that I used to place the rest of the animals and it lined up perfectly. Monkey lined up with a tree, the dragon lined up with the mountain which emphasizes hugeness as a major trait. Pig lined up with yang water and is famous in the saying "sweat like a pig." Sweat is yang water! All these intuitive associations were present after applying the method that I'll describe.
The four animals that I had correctly placed were: rat in cancer, ox in leo, tiger in libra, and hare in taurus. All the rest were incorrect. For the longest time, I had dog associated with Aquarius. At this point, I decided to look for inspiration in the Chinese Zodiac story of the Great animal race. This was the first time that I consulted the story. Luckily enough for me, the animals that I had correct were the first four finishers in the story of the race, and this revealed a pattern for the rankings of the animals in the story.
In the story the animals finished the race in this order from first place to last place: rat, ox, tiger, hare, dragon, snake, horse, ram, monkey, rooster, dog and pig.
The first part of the pattern is that when you take the planet exalted in the chosen sign, it represents the zodiac animal. For example, moon in taurus represents the rat! The reason being that rat is associated with cancer and the moon is the ruler of cancer. So in other words, the moon is the rat and it is exalted in taurus.
The second part of the pattern is that you start with the moon in taurus and, going clockwise, touch upon all the exalted planets in the signs. You will discover that the order of the planets are the same as the order of the rankings of the zodiac animals in the race. The planet that is associated with the animal determines the sign that is associated with the animal, sometimes in a definite manner and sometimes it narrows it down to a 50/50 about where the animal should be associated.
Like I said before, I was lucky to have the first four finishers of the race in the correct signs. So I just happend to notice that: rat ruled cancer, with the moon exalted in taurus. Going clockwise, the next exalted planet is the sun in aries. The ox was associated with leo, so the sun in aries represented the ox who placed second in the great zodiac race. The next exalted planet is venus in pisces. Venus rules two signs: taurus and libra. So, the next two animals to finish in the race would be associated with these two signs. The two animals were the tiger and the hare. I already had the tiger associated with libra and the hare associated with taurus.
This pattern made it clear to me that all I had to do was continue going clockwise and evaluate the exalted planet to see which animal belonged in the associated sign. All the rest of my animal placements were wrong up to this point. With the next exalted planet being mercury in aquarius, now gemini and virgo were on the table. The next animals in the rankings were dragon and snake. I had it narrowed down to 50/50 . Dragon would be either gemini, or virgo and snake would take the other sign. I looked at the element that I had associated with gemini and it was yang earth. This was symbolized by the mountain and was noted by hugeness. The hugest animal in the zodiac is the dragon. With this kind of reasoning and a good reading through of the sign, the element and animal description, I settled with dragon in gemini and this left snake to virgo. Snake in virgo fit well as the snake was described as a healer, and fast calculater. Both of these traits were of virgo.
The next planet was mars in capricorn. Mars also ruled two signs. The next animals were horse and ram. I settled on horse for aries and ram for scorpio.
Mars is exalted again in sagittarius, but I just skipped over that because it was already complete.
The next exalted planet is uranus in scorpio. The next animal is the monkey. This placed monkey to aquarius.
The next exalted planet is saturn in libra. Aquarius was already done, so only capricorn was left. The next animal was the rooster and this placed rooster in capricorn. The bird went to the heavens.
Mercury in virgo was already done with.
Neptune in leo was very specific to pisces, and the next animal was the dog, thus dog was associated with pisces.
Lastly was jupiter in cancer, the last animal was the boar and the only sign left was sagittarius.