A while ago I took part in the breakthrough junior challenge and before I settled on one topic (about brain and meditation). I tried to explain two other topics and later understood I myself didn't understand one topic and the other one was not so "sciencey". I didn't want them to go to waste so here's one (the one I didn't quite understand myself) for you to read and laugh at how dumb my science articles are.
Cats: the internet is filled with their videos. Dogs: more like man is dog's best friend.
Animals are cute and loved. Also admired (tiger picture) or even feared (hyena). They all do have something bizarre in common, they are related because of their fur patterns! "How?! You're nuts" might me the first thought to pop up in your mind since there are myriad animal patterns in the world that seem nowhere to be related but trust me, they're all related. All the beautiful and intricate patterns on the animals boil down to one equally beautiful and elegant equation in math: the reaction-diffusion equation. Not only does this equation predict the fur pattern on animals but also tells us how our fingers are the way they are: divided into five. It can also explain brain tumors to the ecology of a predator-pray population! But since we can't cover everything that this versatile equation can predict, let's cover the basics of two prominent ones: animal fur pattern and the formation of limb digits in tetrapods (whoa getting fancy there) it just means how fingers and toes are formed in four legged animals!
Basically this is the overview of the reaction-diffusion equation:
In a plane with a certain boundary, either homogeneous or not, based on the levels of producers or activators and degraders or inhibitors and the rate diffusion that's occurring, a pattern can be predicted. The area of the plane is also a factor of the pattern produced.
This simple equation can lead to the prediction of all kinds of intriguing patterns on the animals!
Let's look at how the reaction-diffusion equation explains a spotted pattern.
When a certain compound that is an activator exists, there also exists an inhibitor to control it. Just like the predator-pray relationship in nature. Excess of any can lead to disparities or a complete collapse. Let's represent our activators with letter A and inhibitors with letter I. Logically, when there are a lot of mice, there would be cats around to pray on them. The mice population would generally be in a larger ratio to the cat population. For the weaker animals-here the mice-to defend themselves against the stronger ones(the cats), they exist in large groups. The cats try to spread throughout the region in which the mice are around to get more access of eating them. This is the case of inhibitors and activators too, expect no one is trying to eat anyone here. Activators usually form a cluster with inhibitors around them. The pigments, when arranged according to this in a larger area, result in a spot. For stripes to form, a narrower area us usually needed. The pattern formation only extends on the x-axis and results in stripes. You can see this is quote evident in a cheetah. Now you know how a cheetah gets its spots! During instances when clusters of activators and inhibitors are close enough for the activators in one cluster to leak out and connect with the ones in another one, such kind of a pattern is witnessed. "The reaction-diffusion equation efficiently explains how different levels of morphogens result in different, well, results but how on earth does it explain why we have five fingers?!" You might be thinking. Well the answer is definitely not simple.
In the tetrapod's embryo, let's just consider humans here, during the developmental stages in the womb, there's so much stuff going on. Chemicals reacting with each other everywhere and changes happening all the time. During such a chaotic process, the development of fingers relies on the reaction-diffusion equation. First the limbs start of as a blob of cells called limb bud mesenchyme. Here is where proteins such as BMP cause apoptosis or controlled cell death. When BMP is blocked, no cell death occurs. Using the reaction-diffusion equation, a pattern can be made in which there occurs both BMP secretion and blockage causing the blob limb to have a striped pattern, eventually leading to columns of live cells and dead cells. The dead cells leave spaces in between, divding the limb bud into 5 strips and volia! They are the fingers!
The simple equation can connect many fields of science together and help predict the various possibilities of patterns out there in our world, all developed by one ingenious man named Alan Turing. For such a positive contribution to the world, the world didn't positively respond back to him and lead to his death by punishing him for being gay. Let's not forget his work and let's try to carry forward the ideas he put forth by testing out the turing reaction-diffusion equation in various fields of science!
