What is the Rhenish fan in the study of German dialects?

In the study of German dialects, the Rhenish fan refers to the geographical area along the Rhine River where various isoglosses—lines marking the boundaries of specific linguistic features—spread out and diverge.1

These lines represent the varying reach of the High German consonant shift, a historical process where voiceless stops (p, t, k) shifted to fricatives or affricates in the south and spread northward to varying degrees. Because these individual sound changes did not all stop at the same geographic boundary, they create a "fanning out" effect on a map.1

For example, the boundary between Low German and High German is often defined by the maken/machen line, but other shifts—such as those seen in words like Dorp/Dorf or dat/das—did not extend as far north, resulting in the distinct, fanned pattern of dialect boundaries characteristic of the Rhineland.1