FrameTicks->Automatic in ClickPane causes constant processor activity

Question

I discovered that a MatrixPlot in a ClickPane causes one of my processor cores to cycle at about 50% activity if the option FrameTicks -> Automatic is present. I have cut down the code to the following (which doesn't do anything really):

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

Switching to FrameTicks -> None stops the core activity.

To study the processor behavior I let a Clock cycle between None and Automatic every 20 secs (remove the above ClickPane first):

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

This gives me the following processor activity display:

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

My questions are:

• Is this reproducible on other systems?
• Am I doing something wrong or is this a bug?
• Why does the bare MatrixPlot[a] (without any FrameTicks setting whatsoever) have these odd-looking frame tick choices?

Answer 1

Win XP Mma 8.0

The missed peaks correspond to times when the notebook was hidden by another window. Losing focus does not stop the CPU draining.

Answer 2

It seems that the Automatic setting of the FrameTicks option changes an internal variable that can be seen by Dynamic. It is apparently (and I think erroneously) not localized. This causes a complete re-evaluation of the argument of the Dynamic.

A workaround would be to add Refresh, which enables the use of TrackedSymbols, so that we can restrict triggering to just the variables we're interested in, in this case array a and the FrameTicks options value ft:

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

My processor status stays flat at close to zero now.

Answer 3

Confirmed also on Mac OS X 10.6, Mathematica 8.0.1.

I thought at first that this was something to do with the kernel having to recalculate where the ticks went, every time FrameTicks->Automatic option was set.

So I tried this and got the same result. Likewise 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 the 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 surmise that there must be some inefficiency in the way FrameTicks are displayed on these raster-type plot.

In answer to your third question, the odd tick choice doesn't reproduce on my system.