four parametric projection ifs types
- To: mathgroup at smc.vnet.net
- Subject: [mg101649] four parametric projection ifs types
- From: Roger Bagula <rlbagula at sbcglobal.net>
- Date: Sun, 12 Jul 2009 05:51:47 -0400 (EDT)
- References: <h2fe37$ppu$1@smc.vnet.net> <h340hn$gcn$1@smc.vnet.net> <h3760n$f2i$1@smc.vnet.net>
http://www.geocities.com/rlbagulatftn/limacon_kiss.gif So far there are four working parametric ifs projection types: circle-ellipse piriform-drop lemniscape limacon There are two ways to get a kissing Limacon: inner and outer: Mathematica: Clear[f, dlst, pt, cr, ptlst, x, y] RandomSeed[]; dlst = Table[ Random[Integer, {1, 2}], {n, 250000}]; f[1, {x_, y_}] := N[ {(1 - 2*(x2 - y2)/(y2 + x2))*2*x*y/(x2 + y2) , ( 1 - 2*(x2 - y2)/(y2 + x2))*(x2 - y2)/(y2 + x2)}]; f[2, {x_, y_}] := N[{-x/(1/0.085) - y/((1/0.085)), -1/2 + x/((1/0.085)) - y/( 1/0.085)}]; pt = {0.5, 0.75}; cr[n_] := If[n - 2 == 0, RGBColor[0, 0, 1], If[n - 3 == 0, RGBColor[0, 1, 0], If[n - 1 == 0, RGBColor[1, 0, 0], RGBColor[0, 0, 0]]]] ptlst = Table[{cr[dlst[[j]]], Point[pt = f[dlst[[j]], Sequence[pt]]]}, {j, Length[dlst]}]; Show[Graphics[Join[{PointSize[.001]}, ptlst]], AspectRatio -> Automatic, PlotRange -> All] http://www.geocities.com/rlbagulatftn/limacon_2ndkiss.gif MATHEMATICA: Clear[f, dlst, pt, cr, ptlst, x, y] RandomSeed[]; dlst = Table[ Random[Integer, {1, 2}], {n, 100000}]; f[1, {x_, y_}] := N[ {(1 - 2*(x2 - y2)/(y2 + x2))*2*x*y/(x2 + y2) , ( 1 - 2*(x2 - y2)/(y2 + x2))*(x2 - y2)/(y2 + x2)}]; f[2, {x_, y_}] := N[{- x/(1/0.255) - y/(1/0.255), -1/2 + x/(1/0.255) - y/(1/0.255)}]; pt = {0.5, 0.75}; cr[n_] := If[ n - 2 == 0, RGBColor[0, 0, 1], If[n - 3 == 0, RGBColor[0, 1, 0], If[n - 1 == 0, RGBColor[1, 0, 0], RGBColor[0, 0, 0]]]] ptlst = Table[{cr[dlst[[j]]], Point[pt = f[dlst[[j]], Sequence[pt]]]}, {j, Length[dlst]}]; Show[Graphics[Join[{PointSize[.001]}, ptlst]], AspectRatio -> Automatic, PlotRange -> All] http://www.geocities.com/rlbagulatftn/lemniscape_kiss_iff.gif A kissing lemniscape fractal ifs: Mathhematica: Clear[f, dlst, pt, cr, ptlst, x, y] RandomSeed[]; dlst = Table[ Random[Integer, {1, 2}], {n, 250000}]; f[1, {x_, y_}] := N[ {Sqrt[Abs[(((2*x)2 - (2*y)2)/((2*y)2 + (2*x)2))]]*2*x*y/( x2 + y2) , Sqrt[Abs[(((2*x)2 - (2*y)2)/((2*y)2 + (2* x)2))]]*(x2 - y2)/(y2 + x2)}]; f[2, {x_, y_}] := N[{-x/(1/0.370) - y/(1/0.370), 1/2 + x/(1/0.370) - y/(1/0.370)}]; pt = {0.5, 0.75}; cr[n_] := If[ n - 2 == 0, RGBColor[ 0, 0, 1], If[n - 3 == 0, RGBColor[0, 1, 0], If[n - 1 == 0, RGBColor[1, 0, 0], RGBColor[0, 0, 0]]]] ptlst = Table[{cr[dlst[[j]]], Point[pt = f[dlst[[j]], Sequence[pt]]]}, {j, Length[dlst]}]; Show[Graphics[Join[{PointSize[.001]}, ptlst]], AspectRatio -> Automatic, PlotRange -> All]
