What is the technical term for an infinite sentence?

Is there a name for the infinite (repeating, unending) sentence or paragraph? Here is an example of what I mean:

Joe Blow is a chef, painter, author and vocalist from San Francisco who enjoys vinyl records, black and white movies and referring to himself in third-person, as in “Joe Blow is a chef, painter, author and vocalist from San Francisco who enjoys vinyl records, black and white movies and referring to himself in third-person, as in "Joe Blow is a chef, painter, author and vocalist from San Francisco who enjoys vinyl records, black and white movies and referring to himself in third-person, as in "Joe Blow is a chef, painter, author and vocalist from San Francisco who enjoys vinyl records, black and white movies and referring to himself in third-person, as in...........

Your example is a recursive sentence

of, relating to, or constituting a procedure that can repeat itself indefinitely

a recursive rule in a grammar

(MW)

I don't know about the use of recursion in sentences or paragraphs, but there are a number of recursive acronyms used in the IT industry, some notable being PHP (PHP: Hypertext Preprocessor) and as @SGR pointed out GNU (GNU's not Unix).

That is specifically an example of recursion, where something is contained inside itself. It is an foundational concept in the fractal mathematics that form the core of chaos theory, but it would be impossible to ever actually use it in spoken English, at least in the fully expanded form. You could achieve it by reference, as in "This is the sentence I'm talking about" (amusingly enough, both the Google results page itself, and the definition it provides are recursive in this sense).

If something moves forward and then restarts from the beginning isn't that also called a loop?

Oxford Dictionaries
loop: a structure, series, or process the end of which is connected to the beginning.

Wikipedia has an article on infinitive loop

An infinite loop (or endless loop) is a sequence of instructions in a computer program which loops endlessly, either due to the loop having no terminating condition, having one that can never be met, or one that causes the loop to start over.

Remaining on the theme of loop, in art there are many examples in the world of art where the viewer is unable to tell where a sequence began or ended.

M. C. Escher − Drawing Hands, 1948

If we were to imagine that this lithograph came to life, we would see one hand drawing the other continuously. In this situation, neither hand can be identified as being the creator. In fact, Douglas R. Hofstadter in his book I Am A Strange Loop, uses Escher's lithograph to explain his concept of a “strange loop”. Finally, one could compare the OP's sentence and the etching as examples of the eternal dilemma: Which came first, the chicken or the egg?