Turing came up with a theory that was basically an explanation for how a whole bunch of chemicals that are just kind of floating around in space can interact as to create differences from one bit of space to the next. In this way, the seeds of a pattern will emerge. He expressed that process in very abstract mathematical terms. Researchers reported the first experimental evidence that Turing’s theory is correct, by studying the eight evenly spaced ridges that form on the roof of a mouse’s mouth. (People, by the way, have four such ridges on each side, which help us feel and taste food.)
Scientists discovered that in mouse embryos, a molecule called FGF, or fibroblast growth factor, acts as a ridge activator, and SHH, or sonic hedgehog, acts as an inhibitor. When the researchers turned off FGF, the mice formed faint traces of the ridges that are normally made. Conversely, when they turned off SHH, the ridges morphed into one big mound. Changing the expression of one of these partners influenced the behavior of the other—just as Turing’s equations predicted
1. patterns of life
In mathematical terms Turing’s model can be described as:
where: C (x,t) is a vector function of chemical concentration depending on time (t) and position (x). D is the diagonal matrix of diffusion coefficients. f is the vector of reaction kinetics
2. mathematical theory:
All patterns in nature might be describable using this mathematical theory. How did Alan Turing influence how we see the natural world?
3. math modeL:
Scientists discovered that in mouse embryos, a molecule called FGF, or fibroblast growth factor, acts as a ridge activator, and SHH, or sonic hedgehog, acts as an inhibitor. When the researchers turned off FGF, the mice formed faint traces of the ridges that are normally made. Conversely, when they turned off SHH, the ridges morphed into one big mound. Changing the expression of one of these partners influenced the behavior of the other—just as Turing’s equations predicted.
4. Nature explained by numbers
A movie inspired by numbers, geometry and nature, by Cristóbal Vila.
The Fibonacci sequence is one of the most famous formulas in mathematics.
Each number in the sequence is the sum of the two numbers that precede it. So, the sequence goes: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on.
The mathematical equation describing it is Xn+2= Xn+1 + X