M. C. Escher was an artist famed for the drawings he created based on tessellations, or patterns that can repeat indefinitely without gaps or overlap. You can also create animal tessellations by experimenting with stylized animal shapes to find sections that can border each other perfectly. One approach is to cut pieces out of a paper square and tape the cutouts on to the opposite edge of the paper. For more advanced tessellations, try rotating or offsetting the individual shapes.
Fish present obvious opportunities for tessellations. A fish head can fit perfectly into a fish tail with very little modification, allowing an endless row of fish. These rows can be slightly offset relative to one another so that the upper and lower fins of the fish fit into the top and bottom gaps just ahead of the tail. Another approach is to rotate fish, arranging them to fit in sets of three which are fundamentally triangular, and then tessellating tiles of three fish each.
Birds, like fish, have a balanced set of gaps and protrusions that you can fit together without too much difficulty, though you may need to offset, rotate or reflect certain bird shapes. Mirror image birds flying past one another, for example, is a well-known motif in Escher's work. You can also intermingle different types of birds, or for an interesting challenge try to create a tessellation out of birds whose basic shape is tall and skinny, like storks, or birds with long, curved necks, like swans or flamingos.
Many mammals are asymmetrical when viewed from the side, making them hard to tessellate. One solution is to represent legs by dividing a single edge instead of by drawing two or four separate legs, which would be difficult to match to the animal's back. Animals with irregular backs, like camels, or necks, like giraffes, may be easier to tessellate. Another solution is to use mammals that are curled up or resting, providing smoother edges to work with. In a pinch you can interweave the legs of two rows of mammals by turning one row upside down.
Insects, spiders, worms and other bugs present a vast variety of opportunities for tessellations. Butterfly wings, for example, are essentially a self-tessellating hourglass shape. You can arrange six- and eight-legged creatures into patterns in which their legs interlock by either rotating or reflecting them. The wavy shape of a worm is probably too easy a tessellation for most purposes, but worms' flexibility provides interesting potential. For example, three worms' curled tails could intertwine, while their heads reach out to border or intertwine with another set of three.