Dr. Katz may just as well have been made using various arrangements of the same handful of looping GIFs. The atmosphere and depth achieved is inverse to the show’s feeble budget. This is an avant-garde child of constraint. As the wikipedia excerpt explains below, this animated style was first developed by educator and producer Tom Snyder:

The show was computer-animated in a crude, easily recognizable style produced with the software Squigglevision (a device Snyder had employed in his educational animation business) in which all persons and animate objects are colored and have constantly squiggling outlines, while most other inanimate objects are static and usually gray in color.

The original, underlying premise of Dr. Katz is one of economical delivery: stand-up comics appear on the show as Jonathan Katz’s patients, reciting their acts with minor writing adjustments to fit the overarching therapy schtick. When production company Popular Arts turned to Snyder (a boyhood friend of one of the executive producers) to use Squigglevision, the intent was to find an equally economical means of adapting the show for cable without investing in traditional animation processes. The collaboration between Popular Arts, Snyder, and comedic writer Jonathan Katz thus resulted in an austerely crafted cartoon with a nonetheless mesmerizing aesthetic quality.

The secondary challenge was how to affordably animate on cable TV at the time.

Read more on Wikipedia, or just go watch the show on youtube.