DD1 was 4 in January.
She draws flowers by drawing a circle and adding a series of petals, a stem and leaves. She then almost always adds a sun with pointy rays, She draws people who have arms and legs, faces with eyes and a nose but until last week these were connected - she's only just started adding bodies in! And she draws hearts. Lots of hearts. Very occasionally she does other things (like animals), but not often. She likes to stick with what she knows!!!
She can write her name, and Mummy and Daddy. And form most numbers and letters. But she spends hours doing it - she loves it. My mum came to stay recently, and then went to an important meeting at work, opened her diary, and found the page she needed covered in DD's name - the perils of leaving pencil and paper in reach!
I would say as long as he's holding a pencil correctly, then you really don't need to worry. If you do want to do something, maybe try chalks on paving stones rather than paper and pencil? And for writing - well, he won't write unless he recognises letters. So maybe just chat with him about letters as you do things ("That says DS which means I know it's yours - look, that letter there is X which is how your name starts" etc using sounds rather than names, so 'a' sounds like 'ant' rather than 'hay') so he gets the idea that the random lines aren't random, but have some meaning. That's the hardest bit about writing - learning that the shapes have sounds attached to them which are consistent, and that you can read them, hear the sounds and form words. So pick out a few key letters (like the ones in his name) and if you are reading to him, pick them out sometimes, point them out to him, give him the sound and be all surprised that you've found yet another 'e' or 's'. But don't do too many or he'll lose interest. If he doesn't understand that there is a connection between the shape of the letter and the sound and that it is the same (ish!) every time he sees that letter, then him learning to write the letter is no more meaningful than you copying out Chinese characters.
I'd also say don't turn it into a chore - he'll be turned off it. You can encourage but if he's not interested then he's not interested - plenty of kids aren't. He'll get there when he's ready.