Birendra Kumar Nayak

Learn More
This paper deals with the theory and application of 2-Dimensional, nine-neighborhood, nullboundary, uniform as well as hybrid Cellular Automata (2D CA) linear rules in image processing. These rules are classified into nine groups depending upon the number of neighboring cells influences the cell under consideration. All the Uniform rules have been found to(More)
In this paper the theory of Carry Value Transformation (CVT) is designed and developed on a pair of n-bit strings and is used to produce many interesting patterns. One of them is found to be a self-similar fractal whose dimension is same as the dimension of the Sierpinski triangle. Different construction procedures like L-system, Cellular Automata rule,(More)
-The notion of Carry Value Transformation (CVT) is a model of Discrete Deterministic Dynamical System. In this paper, we have studied some interesting properties of CVT and proved that (1) the addition of any two non-negative integers is same as the sum of their CVT and XOR values. (2) While performing the repeated addition of CVT and XOR of two(More)
In this paper the theory of Carry Value Transformation (CVT) is designed and developed on a pair of n-bit strings and is used to produce many interesting patterns. One of them is found to be a self-similar fractal whose dimension is same as the dimension of the Sierpinski triangle. Different construction procedures like L-system, Cellular Automata rule,(More)
In this paper we have defined two functions that have been used to construct different fractals having fractal dimensions between 1 and 2. More precisely, we can say that one of our defined functions produce the fractals whose fractal dimension lies in [1.58, 2) and rest function produce the fractals whose fractal dimension lies in (1, 1.58]. Also we tried(More)
In this paper we have used one 2 variable Boolean function called Rule 6 to define another beautiful transformation named as Extended Rule-6. Using this function we have explored the algebraic beauties and its application to an efficient Round Robin Tournament (RRT) routine for 2 (k is any natural number) number of teams. At the end, we have thrown some(More)
In this paper, the notion Affine Discrete Dynamical Systems (ADDS) in terms of Integral Value Transformations (IVTs), is introduced and their mathematical properties, particularly their equilibrium and stability as a dynamical system, are studied. It is shown that some ADDS are Collatz-like, which generate fractals. It is also shown that ADDS can model(More)
In this paper, a set of transformations is defined on to. Some basic and naïve mathematical structure of is introduced. The concept of discrete dynamical systems through IVT and some further research scope of IVTs are highlighted. and 4]. A class of discrete transformations on named as Integral Value Transformations (IVT), corresponding to each of those CA(More)
2 P. G. Department of Mathematics, Bhubaneswar 751004, India Emails: sarimif@gmail.com, ananyaaroy1@gmail.com, pabitrapalchoudhury@gmail.com and bknatuu@yahoo.co.uk Abstract Integral Value Transformations (IVTs) is a class of continuous maps in a discrete space { } In this paper, these IVTs are considered to be Discrete Dynamical System maps in the space(More)
In this paper, we analyze the algebraic structure of some null boundary as well as some periodic boundary 2-D Cellular Automata (CA) rules by introducing a new matrix multiplication operation using only AND, OR instead of most commonly used AND, EX-OR. This class includes any CA whose rule, when written as an algebra, is a finite Abelean cyclic group in(More)