(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 6858, 165] NotebookOptionsPosition[ 6417, 146] NotebookOutlinePosition[ 6758, 161] CellTagsIndexPosition[ 6715, 158] WindowFrame->Normal ContainsDynamic->True *) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Project - Moir\[EAcute] Patterns", "Section", CellChangeTimes->{ 3.4612562964071407`*^9, 3.461682317732991*^9, {3.461963778667519*^9, 3.461963782196739*^9}, {3.46196449800065*^9, 3.4619645004331207`*^9}, 3.465932545349743*^9}], Cell[TextData[{ "Many interesting effects are obtained by overlapping two identical \ transparencies. For example in this ", StyleBox["Manipulate", "Input"], ", there are two patterns of 20 concentric circles. The center of one of \ these patterns can be moved. When the two patterns are not directly on top of \ each other, dark and light bands appear. This is called a Moir\[EAcute] \ pattern. This particular pattern has an importance to physicists -it is the \ interference pattern created by two nearby (radio, sound, light) transmitters \ operating at the same frequency.\n\nThe project is to extend this ", StyleBox["Manipulate", "Input"], " so that the number of circles (and or the spacing) can be varied. The \ thickness of the circle will have to vary proportionally. The effect should \ be most conspicuous when the thickness of the black circle and the white \ spaces between them are equal." }], "Text", CellChangeTimes->{{3.465920756880628*^9, 3.465920770004315*^9}, { 3.46592083572008*^9, 3.4659209045223093`*^9}, {3.4659209437437143`*^9, 3.465921026514188*^9}, {3.465921105602344*^9, 3.465921309929674*^9}, { 3.4659215122283363`*^9, 3.46592167317533*^9}}], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`c$$ = { 1.3200000000000005`, -0.09999999999999862}, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`c$$], {0, 0}}, Automatic}}, Typeset`size$$ = { 600., {298., 302.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`c$$ = {0, 0}}, "ControllerVariables" :> {}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Graphics[{ Thickness[0.01], $CellContext`circs[{0, 0}], $CellContext`circs[$CellContext`c$$]}, PlotRange -> 25, ImageSize -> 600], "Specifications" :> {{{$CellContext`c$$, {0, 0}}, Automatic, ControlType -> Locator}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{642., {323.375, 328.625}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>({$CellContext`circs[ Pattern[$CellContext`c, Blank[]]] := Table[ Circle[$CellContext`c, $CellContext`r], {$CellContext`r, 20}]}; Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{ 3.465919716837693*^9, 3.465919888775568*^9, {3.465919969639876*^9, 3.465920029203722*^9}, {3.4659200695535717`*^9, 3.465920082434916*^9}, 3.465920178960924*^9, 3.465920251834955*^9, 3.465920292534884*^9, 3.4659203521450768`*^9}], Cell[TextData[{ "It would be nice to have some radio buttons on the ", StyleBox["Manipulate", "Input"], " that control the colors of the circles. Like this example:" }], "Text", CellChangeTimes->{{3.4659234131936703`*^9, 3.465923483811419*^9}}], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`c$$ = {2.0800000000000005`, 0.4000000000000014}, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`c$$], {0, 0}}, Automatic}}, Typeset`size$$ = { 600., {298., 302.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`c$$ = {0, 0}}, "ControllerVariables" :> {}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Graphics[{ Thickness[0.01], Red, $CellContext`circs[{0, 0}], Blue, $CellContext`circs[$CellContext`c$$]}, PlotRange -> 25, ImageSize -> 600], "Specifications" :> {{{$CellContext`c$$, {0, 0}}, Automatic, ControlType -> Locator}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{642., {323.375, 328.625}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>({$CellContext`circs[ Pattern[$CellContext`c, Blank[]]] := Table[ Circle[$CellContext`c, $CellContext`r], {$CellContext`r, 20}]}; Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{ 3.465921855384984*^9, 3.465921911598823*^9, {3.465921944796344*^9, 3.465921994651113*^9}, 3.465922025939135*^9, 3.4659220572686987`*^9, { 3.465923358848428*^9, 3.465923376830653*^9}}] }, Open ]] }, WindowSize->{1024, 668}, WindowMargins->{{10, Automatic}, {Automatic, 0}}, FrontEndVersion->"6.0 for Mac OS X PowerPC (32-bit) (April 20, 2007)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[590, 23, 243, 4, 67, "Section"], Cell[836, 29, 1186, 19, 101, "Text"], Cell[2025, 50, 2084, 43, 670, "Output"], Cell[4112, 95, 248, 5, 26, "Text"], Cell[4363, 102, 2038, 41, 670, "Output"] }, Open ]] } ] *) (* End of internal cache information *)