Cetus was just about to eat poor Andromeda when Perseus showed up and began to battle the sea monster. The fight continued for quite some time until Perseus took the head of Medusa out of the bag he was carrying and, without looking at it himself, showed it to Cetus. As was true with anyone looking at Medusa, the monster immediately turned to stone. The astronomical connection between these two constellations has to do with a special type of star found within them. The star is known as a variable star, one that appears to change brightness.
Stars can be variable for many reasons.
As we have seen, Algol changes brightness because one star eclipses the other. In the case of the two stars about to be mentioned, the star itself changes. In Cetus, and marked on the star chart, one finds the giant, red star Mira, also known as Omicron Ceti. Mira is the brightest and most famous of the type of variable called a long-period variable. Its brightness changes from about magnitude 3 to magnitude 9 in about 165 days and back again in another 165 days.