Carbon is one of the most abundant elements on planet earth. It can be found on the middle-right side of the periodic table. It has four electrons in its outer valence shell. This makes it a neutral atom, it can either gain or lose a total of four electrons. This makes it the perfect atom to form large chains and structures which are fractal-like.
Carbon in biology:
Carbon likes to bond to other carbon atoms and hydrogen atoms in most cases with covalent bonds. Molecules that consist out of carbon and hydrogen molecules are called ‘’hydrocarbons’’. Chains, rings and other shapes can be created this way. In biology they can be found everywhere and have different purposes. They can interlock with others to create even larger structures. An example is could be amino-acids: they consist of an amine group added to a carboxylic-acid group, this combination can have another group added to it. There are only twenty-one different amino-acids but they can combine with other amino-acids to create protein-chains which make parts of cells such as the general structure but also DNA. These cells have their own way to combine with other to create tissue and eventually muscles and organs. The exact shapes of these depend on the organisms they are part of.
Hydrocarbons are not just useful in biology but they are essential for a particular part of chemistry which focusses on these. In organic chemistry hydrocarbons are used as a framework for a large number of compounds. Since the carbon atoms are connected it is easier to transfer electrons (and thus positive and negative charges), this make them a perfect framework. Functional groups and atoms can be attached to these frameworks to make molecules that can be used in a number of different ways. Fuels, medicines and new materials can all be created this way.
Polymers are found in both biology and organic chemistry. They are chains of individual pieces (monomers) that have been connected with others. It starts with either a positive or a negative end, a neutral molecule gets grabbed by it and the charge gets transferred to the side of the neutral molecule. This continues until a molecule with opposite charge. Polyethylene is probably the best known polymers which consist out of ethylene molecules. These polymers can contain variation in their monomers which make them interlock with other polymers. Plastics, fuels and biological structures can be created this way. These can have a multitude of uses, from strong barriers in organisms to plastics and electrically conductive components.
Diamond and silicon carbide (carbon crystals):
Carbon can also form crystals like diamond, silicon carbide and a number of others. Diamonds have naturally been created under immense heat and pressure. The carbon atoms in the crystal are neatly arranged in a grid/lattice (if you ignore impurities). This makes them very strong. Silicon carbide has both carbon and silicon atoms. Because silicon is in the same group as carbon it behaves similarly and will be able to form crystals in the same way, this also requires a lot of heat and pressure. Now, there are always impurities in these crystals. This causes the crystals to grow in ways which causes them to ‘’grow’’ in different directions. Slightly more chaotic fractal-like structures get created this way. Carbon crystals in general are very useful. In chemistry activated coal is used to extract molecules out of solutions. This is made possible by the large surface area which has been created by the fractal structure of the crystal. It is for example possible to remove the colour from red wine by adding activated carbon to it and them filtering it out. The molecules the cause the colour will have gotten stuck in the small holes in the crystal of the activated carbon. These crystals are also very dark, this is because the photons that hit the crystal get bounced around so many times in the structure that it loses a large amount of energy and will not be able to emit visible light. Almost all energy gets transferred into the carbon atoms which causes them to vibrate a bit more which heats up the crystal. Eventually, over a period of about a thousand to a million years crystals like these will change and become more chaotic because of entropy. If you leave a diamond long enough it will convert back into coal which will in turn start to react with hydrogen and oxygen in the air.
How is this a fractal?
Most of these things on their own might not look like fractals. But the fact that they all are related to carbon and connect in different ways on so many different scales makes this a perfect example. You start off with some very simple atoms, they form molecules which are part of polymers and other molecular structures like tissues of organisms. These organisms form populations of different species which roam our planet.