No, nothing to do with the pond in Hyde Park - Serpentine is a variation on a Centipede theme, with just a dash of Pacman thrown in as well.
Objective
You control a serpent, which runs about a maze trying to avoid being eaten by other serpents.
You can attack them, but only from the rear, so that you don't have to face their mouths. After a number of attacks they become shorter than you, turn green, and can then be attacked from the front.
Meanwhile, you are attempting to survive long enough to lay some eggs and raise some young. The hostile serpents also lay eggs from time to time, but these are merely there to provide a points scoring feast for you.
These eggs serve another purpose: when a serpent lays one it also loses a segment, and thus will eventually become short enough to be attacked. But if you try laying an egg when you're too short, you will simply lose a life.
So you must roam about the maze, eat the enemy and their offspring, while staying out of trouble and laying your own eggs.
In Play
The action starts immediately, but you'll have to spend an annoying second or two centring up the Vic's screen with the joystick: why can't programmers manage to get the screen to somewhere where you can actually see it?
The graphics and sound are none too wonderful, but at least suffice to make everything distinguishable.
Once you have started, you realise an immediate shortcoming. Pressing the Fire button on the joystick halts everything!
Now this might be very useful if the telephone rings, but on some joysticks it's almost impossible not to press the fire button while you're trying to hold the stick steady.
Having successfully eaten all the serpents, another screen of faster and more vicious snakes appears, and so it goes on, getting more and more difficult, until the inevitable happens and you get eaten.
An original idea (albeit based on two different existing ones), but Serpentine is not too long in losing its initial appeal. Play it at a friend's house by all means, but sadly not a game that I recommend you to purchase yourself.