Hopalong Attractor

300 computations of Hopalong attractors (also known as Martin attractors after their discoverer Barry Martin based at Aston University, Birmingham, UK. They were later popularised by A. K. Dewdney in a 1986 Scientific American article). A point is started at (0, 0) and subsequently hops between elliptic orbits. The system is a 2D, non-linear iterative type as follows:

x(n+1) = y(n) - SIGN(x(n)) * SQRT(ABS(b * x(n) - c))
y(n+1) = a - x(n)

x(0) = 0.0
y(0) = 0.0

The SIGN function returns 1 if its argument is greater than 0, -1 if less than 0, and 0 if equal to 0. The ABS function simply returns the absolute value of its argument. SQRT is the square root function. All are standard math library functions.
Here a,b and c are free parameters that ultimately control the characteristic features of the attractor. In the present case these were allowed to vary pseudo-randomly (there is no such thing as randomness!) between -1 and 1. The images here comprised two million iterations (points), with the point colour being 'randomised' every 50,000 iterations (giving 40 colours in the image)

Best viewed in fullscreen HD (actual resolution 834x834). Makes a nice screen-saver. Maybe I will improve it by smooth-fading between the frames, and even putting some music to it....one day....

Coded in VB. NET

Category:

Science & Technology

Tags:

• Hopalong
• Martin
• Attractor
• Iterative system
• non linear