For CA with compression set, a special algorithm is employed to speed up computation of the subtree of the ``uniform`` states consisting of all 0s or all 1s, when these are on the attractor (it turns out this must be a 1 or 2 state attractor). If a given state is a pre-image of a uniform state, then the given state's rotation equivalents must also be pre-images, and may be computed simultaneously. The first level of the uniform state's tree is organised into groups of equivalents (shown in different colours). The subtree or each representative state in each group at this first level is computed in turn. Each subtree will be completed before the next is started. Successive pre-image fans in each non-equivalent subtree are given a different colour so that a given subtree may have a mix of colours. However equivalent subtrees will be computed and drawn simultaneously, and will be coloured identically.