VI. Orbit Traps This is one of the largest families of coloring algorithms, because it provides so many options for experimentation. In fact, entire software packages have been built specifically to explore this family of coloring algorithms. The basic idea is to choose a region of the complex plane (denoted by T. T is usually defined as a central shape (usually a simply-calculated item, such as a point, line, or circle) and a threshold distance. Everything within the threshold distance of the trap is considered "inside" the trap.The earliest implementations of orbit trap algorithms simply watched for any T it was "trapped" and iteration stopped.)
Figs 5a and 5b. Hypercross orbit trap in the Mandelbrot set (left). Gaussian integers algorithm in a Julia set (right). There are many more variations, however. The first class of variations covers the shape of the trap region, Another class of variations deals with the relationship between the distances of each T. The classical implementation mentioned above stopped at the first z within the threshold distance to _{n}T. Other variations use the last z to enter the trap, or the closest, or the farthest that is still inside the trap. More exotic variations use different methods for combining all distances below the threshold together._{n}The last major class of variations deals with the actual value used to produce the color. The most common method is simply the distance to the trap shape z values related to the trap distances. _{n}With so many variations possible, and so many combinations of variations, it is nearly impossible to predict exactly what results will be achieved. Sometimes it is even difficult to tell a particular image has used the orbit trap algorithm at all. This is one reason this family of algorithms is so vastly popular. NEXT
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