DEMONSTRATION OF UNIVERSALITY OF CELLULAR AUTOMATA

THINGS THAT WE HAD

Phone Clock Voice Recorder Radio Television Camera Typewriter Gramaphone

THING THAT WE HAVE

Mobile Phone

HOW IS IT POSSIBLE TO HAVE SO MANY FUNCTIONS IN ONE DEVICE?IT IS BECAUSE OF THE UNIVERSALITY OF THE MICROPROCESSOR

IT MEANS THAT

If we have an algorithm for any process, then mobile can run it.

FUNDAMENTAL UNIVERSAL MACHINE

Turing machine is known to be universal machine. Any model that can be shown to be equivalent to Turing machine is also universal.

WHAT IS CELLULAR AUTOMATA

Cellular automata is a dynamic system based on few simple rules according to which it evolved in discrete units of time and space.

WHAT IS THIS PROJECT ABOUT

After knowing about the universality of cellular automata, we made several simulations as its demonstration

GOLDBACH CONJECTURE:

Simulate the goldbach conjecture by using cellular automata

How: The initial condition consists of a mirrored list of particles situated at the same positions as the prime numbers. The

particles on the left and right collide at points that represent the sum of the prime numbers associated with the particles.

Why?? Mathematically there is no such generalized proof of glbach conjecture. By using cellular automata we can verify it as ong

as we want.

Why it is better?? Just run and observe without performing any calculation in mathematics.

CELLULAR AUTOMATA BASED HEAT EQUATION

What? Cellular automata based n the heat equation which is the differential equation. Which evolves with time?

How it works?? This is a continuous type of cellular automata. Here the values of a particular cells will not depends on the value of their neighbour discretely

but based on the overall mean value of neighbours’.

Why?? As we know differential equation are difficult to solve so we create a simulation without solving complex mathematical equation. By using

simple rules the behaviour of PDE can be simulated.

Why it is better?? It saves a tedious job of solving complex differential equations. Also less chance of errors because it need only computation based on cellular

automata.

RANDOM NUMBER GENERATOR

What?? Generating random numbers by using cellular automata based on simple rules.

How it works?? Each cell selects the value from its neighbor randomly and changes according to simple

rules.

Why it is better?? Randomness can easily be generated without any complex means by using the simple rules

of cellular automata such as rule 30 and rule 110.