Skip to main content

graphics - Dynamically splitting Disks with Mouseover


I've recently stumbled across this site: Koalas to the Max, and the first thought that came to my mind was "I want to recreate this with Mathematica".


As a first step I tried to create a Disk that splits itself up into four disks, when the mouse cursor touches it. Those four disks should in turn split themselves up. Here's what I have so far:


makeDisks[pos_] := makeDisks[1, pos]

makeDisks[level_, pos_] :=
Module[{
disk = Disk[pos, 1/level]},
Mouseover[Dynamic@disk, Dynamic[disk = makeDisks[level + 1, #] & /@
(pos + # & /@ (1/(2 level)) Tuples[{-1, 1}, 2])]]
]

(* test with the following *)

Graphics[{makeDisks[1]},

PlotRange -> {{-1, 1}, {-1, 1}}]

For the first disk this seems to work just as I want it. For later steps, however, I got the positioning wrong and some of the disks go back to larger ones, when another one is touched. How can these issues be fixed?


As a next step I want to add colors to the disks. Maybe this can be done by using MapIndexed with makeDisks on the ImageData of some image. The colors in each step should probably be the mean values of appropriate subsets of the image data.


Any help to move this little program forward is highly appreciated!



Answer



Here's a simple way using buttons, for some reason AutoAction is not working so you have to click, anyone know why?


nextPos[p_, r_] := {p + # r/2, r/2} & /@ Tuples[{1, -1}, 2]

DynamicModule[{diskList = {{ {0, 0}, 1}}},

Graphics[Dynamic[
Button[{ColorData["Rainbow"][Last@#], Disk @@ #},
diskList = DeleteCases[Join[diskList, nextPos @@ #], #]
,AutoAction -> True
] & /@ diskList]]
]

circles


The coloring is only based on depth (radius)


Basing color on underlying image:



background = ImageCrop[ExampleData[{"TestImage", "Peppers"}], AspectRatio -> 1];

DynamicModule[{diskList = {{{0, 0}, 1}}}, Graphics[Dynamic[
Button[{RGBColor@ImageValue[background,First@#, DataRange -> {{-1, 1}, {-1, 1}}],
Disk @@ #}
,diskList = DeleteCases[Join[diskList, nextPos @@ #], #]
,AutoAction -> True] & /@ diskList]]]

pepper


Using code from @Szabolcs comment it's possible to split the disks without clicking:



(* Create at most 2^6=64 disks in a row *) 
rmin = 2^-6;
DynamicModule[{diskList = {{{0., 0.}, 1.}}}, Graphics[Dynamic[
EventHandler[{RGBColor@ImageValue[background, First@#, DataRange -> {{-1, 1}, {-1, 1}}],
Disk @@ #}
,{"MouseMoved" :>
If[Last@# > rmin, diskList =DeleteCases[Join[diskList, nextPos @@ #], #]]}
] & /@ diskList]]
]

Comments

Popular posts from this blog

front end - keyboard shortcut to invoke Insert new matrix

I frequently need to type in some matrices, and the menu command Insert > Table/Matrix > New... allows matrices with lines drawn between columns and rows, which is very helpful. I would like to make a keyboard shortcut for it, but cannot find the relevant frontend token command (4209405) for it. Since the FullForm[] and InputForm[] of matrices with lines drawn between rows and columns is the same as those without lines, it's hard to do this via 3rd party system-wide text expanders (e.g. autohotkey or atext on mac). How does one assign a keyboard shortcut for the menu item Insert > Table/Matrix > New... , preferably using only mathematica? Thanks! Answer In the MenuSetup.tr (for linux located in the $InstallationDirectory/SystemFiles/FrontEnd/TextResources/X/ directory), I changed the line MenuItem["&New...", "CreateGridBoxDialog"] to read MenuItem["&New...", "CreateGridBoxDialog", MenuKey["m", Modifiers-...

How to thread a list

I have data in format data = {{a1, a2}, {b1, b2}, {c1, c2}, {d1, d2}} Tableform: I want to thread it to : tdata = {{{a1, b1}, {a2, b2}}, {{a1, c1}, {a2, c2}}, {{a1, d1}, {a2, d2}}} Tableform: And I would like to do better then pseudofunction[n_] := Transpose[{data2[[1]], data2[[n]]}]; SetAttributes[pseudofunction, Listable]; Range[2, 4] // pseudofunction Here is my benchmark data, where data3 is normal sample of real data. data3 = Drop[ExcelWorkBook[[Column1 ;; Column4]], None, 1]; data2 = {a #, b #, c #, d #} & /@ Range[1, 10^5]; data = RandomReal[{0, 1}, {10^6, 4}]; Here is my benchmark code kptnw[list_] := Transpose[{Table[First@#, {Length@# - 1}], Rest@#}, {3, 1, 2}] &@list kptnw2[list_] := Transpose[{ConstantArray[First@#, Length@# - 1], Rest@#}, {3, 1, 2}] &@list OleksandrR[list_] := Flatten[Outer[List, List@First[list], Rest[list], 1], {{2}, {1, 4}}] paradox2[list_] := Partition[Riffle[list[[1]], #], 2] & /@ Drop[list, 1] RM[list_] := FoldList[Transpose[{First@li...

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...