Chaos- one that combines aspects of disorder with aspects of form.
There is at most one solutions to a differential equation with given initial conditions.
Newton's world is deterministic
Butterfly effect: If the same equations are solved using initial values of the variables that differ only very slightly from each other, then the differences become amplified until the new solution differs completely from the original one.
Strange attractor: is a complex motion that the system inevitably homes in on, it can be visualized as a shape in the state-space formed by the variables that describe the system. Chaotic systems: can be predicted in the short term but not in long term.
Mathematics has taken its inspiration from these two sources- the real world and the world of human imagination. What matters is the combination.
We are now in the Golden Age of Mathematics.
There is at most one solutions to a differential equation with given initial conditions.
Newton's world is deterministic
Butterfly effect: If the same equations are solved using initial values of the variables that differ only very slightly from each other, then the differences become amplified until the new solution differs completely from the original one.
Strange attractor: is a complex motion that the system inevitably homes in on, it can be visualized as a shape in the state-space formed by the variables that describe the system. Chaotic systems: can be predicted in the short term but not in long term.
Mathematics has taken its inspiration from these two sources- the real world and the world of human imagination. What matters is the combination.
We are now in the Golden Age of Mathematics.