Glides are calculated by iterating the equation until you arrive at a number smaller that the one you started with. This is ok in 3x+1 as all numbers eventually converge on 1, but in other systems like 3x+5 and 3x+7 (see below) it is possible to get stuck in loops based on other numbers. If the smallest member of the loop is larger than the starting number then that number doesn't have a glide.
Every number either glides to a smaller number or ends up in a loop. The pictures on this page are based on the odd glides (the even numbers are ignored). When a loop is found it is represented by a yellow oval with the label "Ln", where 'n' is the smallest member of the loop. Other numbers are coloured according to the remainder modulo 6.
In 3x+1 there are no known loops other than L1, so every number (other than 1) has a glide. In the 3x+5 and 3x+7 systems there are loops with other seeds (L5 and L7 in 3x+7 and L1, L5, L19, L23, L187 and L347 in 3x+5). In these systems not all numbers have a glide, for instance 11 in 3x+5 gets stuck in a loop based on 19 (11 -> 19 -> 31 -> 49 -> 19).
The following illustrations show the glide structure for systems where K=1, 5, 7, 11 and 13 for odd numbers in the range 1-199.
L347 shows up colourless as it is outside the range 1-199, a quirk of the program I wrote to construct these diagrams.
