plotting - How to create a Disk with smoothly changing coloring?

I want to have a disk. But this disk shouldn't have a fixed color; instead, I'd like it's color to fade smoothly.

Until now, I came up with two ideas how to achieve this.

Idea #1:

smoothlyFadingColorDisk1[r_] := 
 DensityPlot[Max[0, r - Sqrt[x^2 + y^2]], {x, -r, r}, {y, -r, r}, 
  ColorFunction -> (Opacity[#, Purple] &)]

Problems:

It displays axes, and Axes->False won't remove them. This is meant to be just a part of a more complex graphics, so the axes are here completely inaproppiate. (blocking problem)

This makes no sense semantically. I want a Disk (a simple image), not a plot.

Idea #2:

smoothlyShiftedColorDisk2[r_, n_] := 
 Graphics[Flatten@
   Prepend[{Thickness[1/(2*n - 1)]}]@
    Table[{Opacity[(n - i + 1)/n, Purple], 
      Circle[{0, 0}, (i - 1/2)*r/(n - 1/2)]}, {i, 1, n}]]

Problems:

It looks bad at some values of n and horrible at others. This seems to be because for some reason (inaccurate floating point calculations? my mistake in the maths?) the concentric circles are overlapping, and they shouldn't. They should be ideally next to each other. (blocking problem)

I have to manually set the number of colors used (the n variable, number of concentric cirlces). And I'd like Mathematica to take care of this for me, as happens in the first example.

So - neither of these two ideas acheves what I am trying to achieve. Er... How to do this properly?

I have a feeling that this should be possible to achieve in a much simpler way than I was trying to do this...

Comments

plotting - How to draw lines between specified dots on ListPlot?

I would like to create a plot where I have unconnected dots and some connected. So far, I have figured out how to draw the dots. My code is the following: ListPlot[{{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4,13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full] I have thought using ListLinePlot command, but I don't know how to specify to the command to draw only selected lines between the dots. Do have any suggestions/hints on how to do that? Thank you. Answer One possibility would be to use Epilog with Line : ListPlot[ {{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4, 13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full, Epilog -> { Line[ ...

dynamic - How can I make a clickable ArrayPlot that returns input?

I would like to create a dynamic ArrayPlot so that the rectangles, when clicked, provide the input. Can I use ArrayPlot for this? Or is there something else I should have to use? Answer ArrayPlot is much more than just a simple array like Grid : it represents a ranged 2D dataset, and its visualization can be finetuned by options like DataReversed and DataRange . These features make it quite complicated to reproduce the same layout and order with Grid . Here I offer AnnotatedArrayPlot which comes in handy when your dataset is more than just a flat 2D array. The dynamic interface allows highlighting individual cells and possibly interacting with them. AnnotatedArrayPlot works the same way as ArrayPlot and accepts the same options plus Enabled , HighlightCoordinates , HighlightStyle and HighlightElementFunction . data = {{Missing["HasSomeMoreData"], GrayLevel[ 1], {RGBColor[0, 1, 1], RGBColor[0, 0, 1], GrayLevel[1]}, RGBColor[0, 1, 0]}, {GrayLevel[0], GrayLevel...

Is there a way to do conditional matrix loop using 'continue'

I have the following: n = 3; m = 5; ww = RandomReal[{0, 0.1}, {n, n}]; uu = RandomReal[{0, 1}, {m, n}]; pp = RandomReal[{0, 1}, {n, n}]; ss = RandomInteger[{0, 5}, {m, n}]; Grid[{{"ww", "uu", "pp", "ss"}, {ww // TableForm, uu // TableForm, pp // TableForm, ss // TableForm}}, Spacings -> {5, 2}, Dividers -> All] where I would like to look at every element of matrix ss and produce a matrix tt , with zeroes at the locations in ss which have zeroes, and in all other positions do the following: tt = (-1/Subscript[ww, m]) Log[(1 - uu)/(Subscript[pp, m - 1])], where Subscript[ww, m] is the value at index of ww matrix and where Subscript[pp, m - 1] is the value at index-1 of pp matrix. So for example if the first value ever read from matrix ss happens to be 2, then value taken from matrix ww would be from the row 2, but from pp would be from row 1. Also how to tell difference between a 0 as a valid value from within the matrix elemen...

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