Perhaps it will help if you tell us the context of your question: Why are you asking? What you mean by the term depends on that context, not on anything we can tell you. (It is your question, not ours!)
Did you read something that said it was difficult or impossible for a computer to generate a pathological function? Tell us where, and quote it. We need to know what they mean by the term.
As you have presumably seen (e.g. here), it is a broad term that can refer to breaking any sort of "rule". Perhaps that in itself would be why they can't be invented by an algorithm, which by definition follows rules. It takes a mathematician's imagination to think such things. (Of course, this also depends on what you mean by "new".)
new = unseen before function.
I don't read some stuff that tell the a function can't be made on computer.
But, I think that In Math every term has a fixed definition.
Can you give me some other source to find information about pathalogical function.
What I read is that: a pathalogical function is under the main subject of paradox.
Here is the article in English:
I. Kleiner and N. Movshovitz-Hadar: The Role of Paradoxes in the History of Mathematics, American Mathematical Monthly. 1994, Vol. 101, No. 10, pp. 963-974.
I can give a link to it if you want.