This article is not only to answer this to you, but it is also an answer for my own self. I am a Cthulhu cultist (specifically) and I seek this question like three months now. But I finally have the answer. I have covered what Dagon represents in nature. Dagon represents the ocean the horrors and the birth of life in it. Shub Niggurath represents life in the woods and mother nature. The Lovecraftian Gaia if you like. Azathoth the Big Bang which started all of the existence. Yog Sothoth represents the infinity in everything. Nug and Yeb represent the Yin and Yang. Nyarlathotep the unknown evil and the darkness in man. The nameless mist represents those things that have to be found. But Cthulhu? What Cthulhu represents when it comes to nature? This is the subject that I am going to cover.
From the Cthulhu Mythos, we know that Cthulhu came from the stars before the reign of man. Starting a war between the Elder Things. What does that mean metaphorically? I will give you a small clue. In the story at the mountains of madness, Leng saw a footprint at a rock more ancient than life itself. But before I go further I need to remind you of my experience with Dagon a long time before. The reason is important because it is based a bit on it. I will be very brief so I will just tell only the point we are going to focus on. The similarity of the word R'lyeh with the words Reality, Real, and especially the word Really. The point was that R'lyeh is not a physical place in the ocean, but our own reality. R'lyeh and so Cthulhu is everywhere around us. Even to our own minds, because we are creations of this reality. But as we know Cthulhu is a sea god how he is everything around us? Well not exactly. He is responsible for it.
Donald Tyson associated him with fire, and I will explain why I mentioned that. Cthulhu is chaotic and this sea that he is sleeping is the void/chaos. Cthulhu as we know is the one who will bring the Old Ones. Well in some way he did. Life needs places that the temperature and the environment are suitable.
The position of the earth in the solar is system is just in the perfect place so life can exist. So to be brief, Cthulhu represents all of this Chaos that existed before life, the creation of this planet, and the rule of chaos for millions of years. All of these happen until things got a bit more in order, and this is where the slumber of Cthulhu started. Dagon (water) "arrived" on earth creating the first lifeforms. Then Shub Niggurath (Plants, trees, etc) and the list goes on and on. We are here because of him. And I am will go deeper. I will go again... to his body. If we look at his body we can confirm that. We can see the four elements. Octopus=Water, Dragon=Fire, Wings=air, Human=Earth. In the Cthulhu Mythos, we see that Cthulhu doesn't have an actual form and he chose to have this form. So this means this. Cthulhu's consciousness= Spirit. This of course leads us to the symbol of the five-pointed star, which represents the elements. But I will save that for later. Tyson said that the color red is associated with Cthulhu. For me not only. And it is not A coincidence. He associated red because of Chaos and because Cthulhu is a warrior god. Plus our Root Chacra which is survival is associated with the color red. It also not a coincidence that many pictures show him with red Eyes. But to be personally they were some greenish-yellow. I will also mention his worship. Do you remember the gathering ritual of The Cult of Cthulhu in the story The Call of Cthulhu? Fire and fire represent Chaos.
Now I will come back to the Elder Sign. The elder sign is actually the pentacle. The elements. And the flaming eye represents the third eye or Anja chakra. As he communicates through dreams. But personally, I think a mouth with teeth would fit better. I remember that the first Cthulhu story I ever read was a Greek book named "The Brotherhood of Cthulhu". The elder sign is the first symbol of the mythos that I ever met. The symbol was used for sacrifices. It was drawn to the ground in a circle with five black candles. At the end of the ritual, they were killing a human inside the circle of the symbol. The protagonist of the story sometimes was calling it, "The symbol of Cthulhu". Well, it makes sense now.
https://www.youtube.com/watch?v=xj7O8mrO_wY&t=1s
https://www.youtube.com/watch?v=55oDyazPdTU
Ia Ia Cthulhu Fhtagn.
~Nythaflythulhu
May They RISE!