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Re: Flat colour in RegionPlot; millions of little triangles

• To: mathgroup at smc.vnet.net
• Subject: [mg81668] Re: Flat colour in RegionPlot; millions of little triangles
• From: ulises <ulises at wolfram.com>
• Date: Mon, 1 Oct 2007 04:44:46 -0400 (EDT)
• References: <fdkqst$7bk$1@smc.vnet.net><fdnlcc$kk6$1@smc.vnet.net>

Use:


RegionPlot[
 Abs[Nest[(#^2 + x + I y) &, x + I y, 16]] < 2, {x, -2, 1}, {y, -1.5,
  1.5}, PlotStyle -> None]


Note that the interior polygons are tere for a reason, for example,
this works as expected:

g = RegionPlot[
  Abs[Nest[(#^2 + x + I y) &, x + I y, 16]] < 2, {x, -2, 1}, {y, -1.5,
    1.5}, PlotStyle -> None]

g2 = g /. {Line[x_] -> {Line[x], Polygon[x]}}


so, why we do not do this by default? well because then this will not
work:

RegionPlot[x^2 + y^2 > 1 && x^2 + y^2 < 9, {x, -3, 3}, {y, -3, 3}]


g = RegionPlot[x^2 + y^2 > 1 && x^2 + y^2 < 9, {x, -3, 3}, {y, -3, 3},
   PlotStyle -> None]

g2 = g /. {Line[x_] -> {Line[x], Polygon[x]}}


you need an interior mesh in order to handle interior holes in
regions, as well as general Mesh lines and other processing of other
options.

Ulises Cervantes
WRI