Attempting to calculate the theoretical maximum score. I think the world is a cylinder, so I will use the formula circumference times height to calculate the surface area.
Circumference we can measure by following a circle and find out when we touch our tail. To not rely on eyeballing a circle we can use the land barriers that are pretty circular. It happens soon to the "end of the game" at ~35 apples. Height we can find by measuring when we touch our own tail by going perfectly centripetal. It happens at ~138 apples. The snake is built from circles, let's assume of radius 0.5/pi, the snake starts with 7 circles and gain a single 1 each time we eat an apple.
Thus, circumference is equal to 42, height to 145, area to 6090. Area of a single circle is 0.25/pi, thus the a maximum score is 2430pi or ~76529. As this measurement cannot measure more precise than 1 circle, the error bars are 42±1 and 145±1 for dimensions, therefore the area is ±187 and the score should be ±748pi which is ±2350.
