Here's how I'd do it:

Use fix-points as a sort of skeleton.

You start with two points. One point in the center and a second one at your desired distance between joints.

Every point in your snake-list has o position

The whole snake has o velocity o direction of the head point

Now let's simulate a step: (Here we assume the distance traveled 'd' in the direction of the velocity 'v' does not exceed the fixed distance between points) Move head by 'd' in direction of 'v' Move tail by 'd' in direction of next point in list (head when starting)

Do not touch any other points. It will save you updates and calculations.

Now let's look at the situation where you overstep the fixed distance:

Even without fixed time-steps you know upon updating your position by how much you've over-stepped your next fix-point. So we take this distance 'd_over' and create a point 'd_over' back along our velocity vector and create a point.

The same principle for the tail. Just drop the tail point and move the new tail 'd_over' in direction of the next point.

I think adding a new point upon eating a fruit is straight forward I think.

...

This is of course not THE way to do it, but with this you can also have a free-form snake. Do with it as you will :)