FrameTicks-> Automatic in ClickPane causes continuous processor activity

Question

I found that a MatrixPlot in ClickPane causes one of my processor cores in the loop to work about 50% if the FrameTicks -> Automatic option is present. I reduced the code to the following (which does nothing):

 a = ConstantArray[0, {2, 11}]; ClickPane[ Dynamic@ MatrixPlot[a, FrameTicks -> Automatic], # & ] 

Switching to FrameTicks -> None stops kernel activity.

To study the behavior of the processor, I give a Clock loop between None and Automatic every 20 seconds (first remove the above ClickPane):

 ClickPane[ Dynamic@ MatrixPlot[a, FrameTicks -> ft], # & ] Dynamic[ft = {Automatic, None}[[Clock[{1, 2, 1}, 20]]]] 

This gives me the following kind of processor activity:

This is on my Win7-64 / MMA 8.0.1 system.

My questions:

• Is it reproducible in other systems?
• Am I doing something wrong or is it a mistake?
• Why do the naked MatrixPlot[a] (without any FrameTicks settings FrameTicks all) have these odd checkmark options?

Answer 1

It seems that the Automatic parameter of the FrameTicks parameter changes the internal variable that can be seen with Dynamic . Apparently (and I mistakenly think) it is not localized. This leads to a complete reevaluation of the Dynamic argument.

The workaround is to add Refresh , which allows you to use TrackedSymbols , so that we can restrict the launch to only the variables of interest to us, in this case the array a and FrameTicks ft :

 ClickPane[ Dynamic@ Refresh[ MatrixPlot[a, FrameTicks -> ft], TrackedSymbols -> {a, ft}], # & ] Dynamic[ft = {Automatic, None}[[Clock[{1, 2, 1}, 20]]]] 

Now my processor status remains zero.

Answer 2

Win XP Mma 8.0

Missing peaks correspond to the times when the laptop was hidden by another window. Loss of focus does not stop draining the processor.

Answer 3

Also confirmed in Mac OS X 10.6, Mathematica 8.0.1.

At first I thought that this was due to the fact that the kernel should recount where the ticks were, every time the FrameTicks->Automatic option was set.

So, I tried this and got the same result. Similarly for ArrayPlot .

 With[{fta = FrameTicks /. FullForm[MatrixPlot[a, FrameTicks -> Automatic]][[1, 4]]}, ClickPane[ Dynamic@MatrixPlot [a, FrameTicks -> ft], # &] Dynamic[ft = {fta, None}[[Clock[{1, 2, 1}, 20]]]] ] 

But not for this plot - CPU usage barely moved between two states:

 ClickPane[ Dynamic@Plot [Sin[x], {x, 0, 6 Pi}, Frame -> True, FrameTicks -> ft], # &] Dynamic[ft = {Automatic, None}[[Clock[{1, 2, 1}, 20]]]] 

I can only assume that in this bitmap image some FrameTicks inefficiency should be displayed.

In response to your third question, choosing an odd tick does not play in my system.