Here is the process:
I found the points of symmetry in Escher’s Lizard (No. 124), which has interesting rotational and reflectional symmetry. After a first failure, I discovered the importance of adding the lopsided grid formed by joining heads and tails – it keeps black and white “squares” from touching too much and presents lines that can be “folded,” so to speak, to form the image.
Then I used graph paper to plot a similar angular reference grid with points of symmetry on the midpoints of “vertical” line segments. The graph paper also helps to make symmetrical changes while working out a design. Gradually, a bat-eared figure emerged – and the bat imagery is appropriate since half the figures are upside down!