interleaved bit-map - definition. What is interleaved bit-map
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THE TRANSFORMATION OF THE UNIT INTERVAL THAT MAPS X TO 2X MOD 1
Dyadic map; 2x mod 1 map; Bernoulli map; Doubling map; Bit shift map; Bit-shift map; Sawtooth map

Bit array         
ARRAY DATA STRUCTURE THAT COMPACTLY STORES BITS
Bit vector; Bitvector; Boolean array; Boolean vector; Bitstring; Bitset; Bit vectors; Bit string
A bit array (also known as bit map, bit set, bit string, or bit vector) is an array data structure that compactly stores bits. It can be used to implement a simple set data structure.
bit string         
ARRAY DATA STRUCTURE THAT COMPACTLY STORES BITS
Bit vector; Bitvector; Boolean array; Boolean vector; Bitstring; Bitset; Bit vectors; Bit string
<programming, data> An ordered sequence of bits. This is very similar to a bit pattern except that the term "string" suggests an arbitrary length sequence as opposed to a pre-determined length "pattern".
Bit (horse)         
  • Horse skull showing the large gap between the front teeth and the back teeth. The bit sits in this gap, and extends beyond from side to side.
TYPE OF HORSE TACK
Horse bit; Horse bits; Champing at the bit; Chomping at the bit; Horse's bit; Horsebit
The bit is an item of a horse's tack. It usually refers to the assembly of components that contacts and controls the horse's mouth, and includes the shanks, rings, cheekpads and mullen, all described here below, but it also sometimes simply refers to the mullen, the piece that fits inside the horse's mouth.

ويكيبيديا

Dyadic transformation

The dyadic transformation (also known as the dyadic map, bit shift map, 2x mod 1 map, Bernoulli map, doubling map or sawtooth map) is the mapping (i.e., recurrence relation)

T : [ 0 , 1 ) [ 0 , 1 ) {\displaystyle T:[0,1)\to [0,1)^{\infty }}
x ( x 0 , x 1 , x 2 , ) {\displaystyle x\mapsto (x_{0},x_{1},x_{2},\ldots )}

(where [ 0 , 1 ) {\displaystyle [0,1)^{\infty }} is the set of sequences from [ 0 , 1 ) {\displaystyle [0,1)} ) produced by the rule

x 0 = x {\displaystyle x_{0}=x}
for all  n 0 ,   x n + 1 = ( 2 x n ) mod 1 {\displaystyle {\text{for all }}n\geq 0,\ x_{n+1}=(2x_{n}){\bmod {1}}} .

Equivalently, the dyadic transformation can also be defined as the iterated function map of the piecewise linear function

T ( x ) = { 2 x 0 x < 1 2 2 x 1 1 2 x < 1. {\displaystyle T(x)={\begin{cases}2x&0\leq x<{\frac {1}{2}}\\2x-1&{\frac {1}{2}}\leq x<1.\end{cases}}}

The name bit shift map arises because, if the value of an iterate is written in binary notation, the next iterate is obtained by shifting the binary point one bit to the right, and if the bit to the left of the new binary point is a "one", replacing it with a zero.

The dyadic transformation provides an example of how a simple 1-dimensional map can give rise to chaos. This map readily generalizes to several others. An important one is the beta transformation, defined as T β ( x ) = β x mod 1 {\displaystyle T_{\beta }(x)=\beta x{\bmod {1}}} . This map has been extensively studied by many authors. It was introduced by Alfréd Rényi in 1957, and an invariant measure for it was given by Alexander Gelfond in 1959 and again independently by Bill Parry in 1960.