The contribution of this paper is a new version of the escape time algorithm adapted to synthesize fractal images, identified with attractors of iterated function systems (IFS). The proposed synthesis algorithm is based on the use of shift dynamics, associated with one or another IFS. The novelty of the algorithm is grounded on two factors. Firstly, the strategy for the separation of extended domains of the inverse affine transformations, specified by IFS, is developed. Secondly, the variable escape time for different points of a synthesized fractal image (IFS attractor) is proposed and explored. Experimental results show that the above two factors ensure uniform rendering of image points (pixels) in colour.