Mirriam-Webster gives this as one of the definitions of "have":

7a: to cause or command to do something — used with the infinitive without to

| have the children stay

As you mentioned, it can be used when you command a person to perform an action. It can also be used when you cause something to perform an action.

In both cases, it is a gentler option than saying "make" while keeping the same meaning. You could say make the picture instantly appear and it would not be incorrect at all, but it sounds a little more forceful. It carries the very slight implication that it is natural for the picture to not appear instantly, and that it must be forced to do so. Compare it to this more dramatic example: I can make John meet you at the entrance sounds like John dislikes this and must be forced to do it. Unless that's what you mean to communicate, it is preferable to say I can have John meet you at the entrance.

Merriam Webster gives this as one of the definitions of "have":

7a: to cause or command to do something — used with the infinitive without to

| have the children stay

As you mentioned, it can be used when you command a person to perform an action. It can also be used when you cause something to perform an action.

In both cases, it is a gentler option than saying "make" while keeping the same meaning. You could say make the picture instantly appear and it would not be incorrect at all, but it sounds a little more forceful. It carries the very slight implication that it is natural for the picture to not appear instantly, and that it must be forced to do so. Compare it to this more dramatic example: I can make John meet you at the entrance sounds like John dislikes this and must be forced to do it. Unless that's what you mean to communicate, it is preferable to say I can have John meet you at the entrance.