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You did not explain (at least to my satisfaction) what this code it supposed to do therefore is hard to give a rigorous answer, but I will attempt to cover multiple issues. First a note: Module[{}, . . . ] is arguably a purposeless construct, one I have no use for and which I remove with every opportunity I get. However at least one very experienced user ...


In Mathematica 10.0: MandelbrotSetPlot[{-2 - I, 1 + I}] (Admittedly, this doesn't address what's wrong with the code in the original question, but if you just want to get a Mandelbrot set plot, surely a built-in function is likely to be reasonably efficient.)


This is an ideal use case for SemanticImport, but unfortunately it has issues getting the commas right in version 10.0. Luckily, version 10.0.1 has already fixed this bug:


I notice some striking similarities between this question and the following two: Calculating a sequence of functions using iteration Multiple generators for iterative construction of fractals Presumably, the user is the same, which conceals information about your mathematical and programming background - information that's useful to potential answers. ...


I worked on Interpreter. As far as the implentation is now, the DelimitedSequence parser does not support quoting, so what you want can't be done. We'll try to add it in a future version.


Your code is redefining the function f every time the Manipulate updates its contents pane, which causing Mathematica to go hyper. You should use the option Initialization so the function is defined just once. Manipulate[ Column @ {Plot[f[x], {x, 0, a}], f[a]}, {a, 1, 50}, Initialization :> (f[x_] = Sin[x])]


It seems the definition of f inside the Manipulate is causing the problem (I'm not sure on the exact details, perhaps someone else can elaborate). Besides eldo's solution with TrackedSymbols, you might opt to define f outside: f[x_] := Sin[x] Manipulate[{Plot[f[x], {x, 0, a}], f[a]}, {a, 1, 50}] But why define f at all? It can also be done without ...


Manipulate[f[x_] := Sin[x]; {Plot[f[x], {x, 0, a}], f[a]}, {a, 1, 50}, TrackedSymbols :> {a}] solved the problem for me (I got the same flickering). The Documentation doesn't say too much about TrackedSymbols. In your case not only a but also x is continiously updateted. But Manipulate should update x only in case a changes, i.e., the slider is moved. ...

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