I have created this site mostly for dumping different unrelated stuff I have. I would be happy, if someone will find something of it interesting, though I am not really aiming this.
You can contact me using this email address:
I am planning to write mostly in English, though some texts will probably be in Russian.
Fibonacci numbers are positive integer values, determined by equation:
First values are 1, 1, 3, 5, 8, 13, 21 ... Here is binary representation of this sequence (black points are 0 and white are 1):
Here is the same sequence, continued: first 1025 fi and first 5000 fi (1.1Mb). Image looks quite chaotic, but it contains interesting visible regularities of triangle form. Almost linear growth of length of binary representation is consequence of exponential growth of fi.
I have just found reference to this procedure somewhere in the Internet and re-calculated it in high resolution, using contemporary software; it is not my invention.
Consider binary image whose pixels with coordinates {i,j} are white (1), if i and j are mutually-prime and black (0), if not. Mutually primes are numbers, whose GCD equals to 1. Here is fragment of this map:
Absolutely rigid balls, colliding inside closed volume, may produdce interesting dynamics. Now, only Java applet, demonstrating moving balls is available. Click here to see applet (Requires Java 1.4 or higher).
Numercal calculation of functional root of funciton, using taylor series. Software used: Python, Octave. Link
