I'm looking for a phrase or expression to describe a certain kind of cognitive bias. Specifically, I have in mind a situation where someone is convinced that something false is actually true, and this leads them to more and more unreasonable beliefs. E.g., someone who is generally reasonable believes the earth is flat (say a few centuries ago, when direct evidence was harder to come by), and when presented with evidence that strongly suggests otherwise, such as visual evidence that the moon is round or the way ships disappear over the horizon, they create a web of convoluted beliefs (which may continue to grow in order to support itself) to explain these effects because their flat-earth belief is so entrenched it doesn't seriously occur to them that that is false.
The closest related terms I can think of are "blind spot" and "ostrich effect." But these terms don't explicitly refer to the act of making up new narratives/beliefs in order to make observations fit your preconceptions about the universe.
Edit: In response to many of the comments and answers, let me try to clarify. It is certainly similar to this question, but what I am ideally hoping for is a phrase (verb, noun, whatever) to describe a gradual process that snowballs, whereby one false belief leads a reasonable person to construct an increasingly warped view of reality. This could be either something extreme driving the person to a completely insane worldview, or a mild quirk where a person just has a very flawed understanding of specialized issue like what is going on with a plumbing problem in their house and a nearby rascally family of gophers. The person's beliefs could be logically consistent or inconsistent, and the person might come to realize their mistake after seeing direct evidence or just accumulating enough second-hand evidence to reach a tipping point. In particular, what I'd like to describe is certainly a consequence of confirmation bias as suggested in one of the answers, but I'd like to more clearly refer to this specific kind of process in which confirmation bias affects one's thinking beyond the original false belief.
(Sorry I don't a have nice pithy illustrative example.)