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    $\begingroup$ That is neat! So what's up with the ticks and labels? M seems to be a bit arbitrary in generating them and it seems to only be dependent on scale $\endgroup$ Commented May 4, 2015 at 23:19
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    $\begingroup$ @LLlAMnYP I agree the generation seems a bit random but it is likely a rather complex problem to handle generally. You can use one of the tools from (1742) to peer at the definitions of Charting`ScaledTicks, Charting`FindTicks, Charting`FindLogTicks etc. to see the process. Ultimately manual generation may be needed for the best visual result. $\endgroup$ Commented May 5, 2015 at 0:19
  • $\begingroup$ Thank you sir, this is pure gold. When I was fiddling around, trying to build custom tick functions, these would always come up in error messages... $\endgroup$ Commented May 5, 2015 at 0:59
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    $\begingroup$ In Mathematica 9, I don't see quite the same behavior. In particular, I have to draw the GridLine at Log[9] rather than just 9 for it to appear at the place labeled 9 in the plot. $\endgroup$ Commented May 5, 2015 at 18:24
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    $\begingroup$ @thecommexokid regarding grid line at Log[9] that is indication of further development of this function which is encouraging, but also indication that one cannot expect it to remain unchanged. Because I chose SubValues notation for fn I cannot use Listable itself as that would only thread over off and scale rather than x_List; this is my workaround. $\endgroup$ Commented May 5, 2015 at 23:04