Re: Plot modular function on unit disk
- To: mathgroup at smc.vnet.net
- Subject: [mg109588] Re: Plot modular function on unit disk
- From: Patrick Scheibe <pscheibe at trm.uni-leipzig.de>
- Date: Fri, 7 May 2010 06:28:25 -0400 (EDT)
Please replace the first "would" with "would not"
Sorry for the typo
Cheers
Patrick
Am May 6, 2010 um 10:51 AM schrieb Patrick Scheibe:
> Hi,
>
> I would use RegionPlot. Why don't you create your raster of pixels
> with
> (Parallel)Table und use ArrayPlot to create the graphics?
> ParallelTable is
> fast and you can create rasters of arbitrary size.
>
> nx=512;
> cmplxFunc[x_, y_] :=
> If[Abs[x + I y] != 0,
> With[{nome = 1/(I Pi) Log[x + I y]},
> If[Im[nome] > 0.009,
> With[{value = KleinInvariantJ[nome]},
> Min[2^15, Max[0, Re[value]]]
> ], 0]
> ], 0]
> DistributeDefinitions[cmplxFunc,nx]
>
> data = ParallelTable[
> cmplxFunc[x, y], {y, -1, 1, 2./nx}, {x, -1, 1, 2./nx}];
>
> ArrayPlot[data,
> ColorFunction -> (If[# == 0., Lighter[Gray],
> ColorData["GreenPinkTones"][#^0.2]] &)]
>
> Please note that you can use triples in ArrayPlot too if you want to
> set
> angle, saturation and brightness of hue:
>
> ArrayPlot[RandomReal[{0, 1}, {3, 3, 3}], ColorFunction -> (Hue[##] &)]
>
> Cheers
> Patrick
>
>
> Am May 3, 2010 um 1:55 PM schrieb Snas:
>
>> I have been using the following algorithm to plot some complex
>> functions in Mathematica. I am trying to get a representation of
>> modular function on the unit disk using Mathematica like in this
>> link (not produced by mathematica)
>> http://en.wikipedia.org/wiki/File:J-inv-real.jpeg
>>
>> I have tried modifying the function below using Cayley transform
>> with no success.
>>
>> I would very much appreciate any suggestions.
>>
>> Sincerely,
>>
>> Snaes
>>
>> ComplexGraph[f_, xmin_, xmax_, ymin_, ymax_, points_: 100] :=
>> (* f is the complex function to be graphed in the region
>> [xmin,xmax] * [ymin,ymax].
>> The parameter points controls how many points will be
>> sampled in each direction;. good values are 100-500. *)
>> RegionPlot[True, {x, xmin, xmax}, {y, ymin, ymax},
>> ColorFunction -> Function[{x, y},
>> Hue[Mod[Arg[f[(I - (x + I*y))/(I + (x + I*y))]], 2 Pi]/(2 Pi),
>> 1/(1 + 0.3 Log[Abs[f[(I - (x + I*y))/(I + (x + I*y))]] + 1]),
>> 1 - 1/(1.1 +
>> 5 Log[Abs[f[(I - (x + I*y))/(I + (x + I*y))]] + 1])]],
>> ColorFunctionScaling -> False,
>> AspectRatio -> Automatic,
>> PlotPoints -> points]
>>
>
>
