why do some thorns point 'up', and other thorns stick out, and other thorns point down...?

It's very much dependent on the predator that the plant is trying to discourage. If a predator is likely to come from below, then the thorns will point downward; if it's likely to come from above, then they'll point upward, and so on. If the plant depends on thorns or "stickers" to transport seed, then it may have lots of points in all directions, like a thistle or cockleburr.

If you mean differences amongst different types of plants, there are a few reasons.

1. Fractals:a plant may be modeled mathematically, such as "on each branch, make a branch 1/2 the size and at 45 degree angle". Such rules can be used to draw realistic looking plants.

2. If the rules change due to mutation or cross-breeding, the rules may produce thorns, rather than leafy branches.

3. Depending on what attacks the plant, those with certain patterns may survive better (e.g. big, widely spaced thorns might deter a mammal or lizard, small, closely space ones would deter insects).

Thorns are there to stop things from eating whatever they are protecting so they will have evolved to deflect whichever animal species is trying to eat the plant. Some might be short, some tall, so the thorns point in that direction.

Down for insects crawling up the stem.

Up for flying insects or birds.

Straight for you and me or other animals

there is no such thing.