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What is a fractal binary pattern?
By converting each positive integer including zero into its respective sequence of vertically-oriented binary digits (1 is black and 0 is white), we get an infinite visual image with self-similarity properties or a fractal binary pattern.
What is the Box Counting Method or BCM for short?
It is a well-known technique used to extract numerical information from an image. Such information is called BCM data points and are used to calculate the fractal dimension of an object. The box counting method was applied to our binary pattern and after carrying out all calculations we obtain a numerical value between one and two thus demonstrating that our visual image is indeed a fractal binary pattern.
What is meant by "mathematical background"?
In physics, the cosmic background radiation is defined as the remnant from the Big Bang. To put it another way, the cosmic background radiation is the physical background for all and any activity since the beginning of time itself. On the other hand, I have presented in my book the concept of mathematical background as the abstract framework underlying any mathematical object. If we assume that mathematics deals with four basic notions: quantity, space, change and structure. The number line is the mathematical background for quantity since with it we can define the natural numbers, the integers and the real numbers.
  
Here is the full index
What is a fractal binary pattern?
What is the Box Counting Method or BCM for short?
What is meant by "mathematical background"?
Why is the distribution of prime numbers hidden within a fractal binary pattern?
What are p-adic numbers?
What is a p-adic universe?
How is the Collatz problem connected to the prime numbers?
Is 3x + 1 the only function that works as a solution to the Collatz problem?
What are probabilistic primality tests?
What are deterministic primality tests?
What are mirror primes?
Can Fermat numbers be defined in terms of primes?
Can the first three odd primes be used to generate other primes?
Can the first four primes be used as a primality test?