It must be a betta thing, all the bettas I've ever owned have had their own little "patterns" as well! My female always swims the whole length of the front of her tank in horizontal lines, back and forth, over and over and over again; and my male likes to swim along the left side of the tank, sort of in circles, under his plants and along the bottom =)
My Current bettas:
Sullivan- Orange rose tail halfmoon male
Daisy- Mustard Gas (black and yellow) veil tail female
Milton- Teal butterfly halfmoon male (mom's betta)
DFTBA to nerdfighters working to decrease world suck!