The repeating patterns in the wikipedia articles on wild arcs and wild knots seem to me to be not continuously deformable to each other. Is this true? For clarity, here is my diagram of the repeating pattern in the wikipedia wild arc diagram. If you follow the curve, you will see it go above/below/above/below/above/below the other parts of the curve in a repeating sequence of 6 crossings. (Ignore the initial 3 crossings.)
By contrast, the wikipedia wild knot curve goes above/above/below/above/below/below in a repeating pattern of six crossings as in the following diagram. (Ignore the initial 3 crossings.)
This second diagram agrees with the book "Topology" by Hocking and Young, Dover 1961, 1988, pages 176–177. They claim that this is what Artin and Fox originally published in 1948. But the wikipedia wild arc article claims that the pattern in my first diagram is what Artin and Fox published.
My question is whether these two knot patterns are equivalent. I don't see how to continuously deform one into the other. And I'm not certain that the complements of these two curves have the same homotopy groups.