# An array of Julia sets

Back to Robert's Math Figures

Code (see the Mandelbrot set code to see how this works, if you're interested):

```gr =
Table[
ListDensityPlot[
Table[-Length[
FixedPointList[ #^2 + a + b I &, x + I y, 35,
SameTest->(Abs[#2] > 2.0 &) ]],
{y, -1.1, 1.1, 2.2/35},{x, -1.1, 1.1, 2.2/35}],
Mesh->False, Frame->False, Axes->False,
AspectRatio->1, DisplayFunction->Identity ],
{a, -2.0, 1.0, 1/3.}, {b, -1.0, 1.0, 1/3.} ];

Show[ GraphicsArray[ Transpose[gr] ] ];```

In Mathematica 3.0 we can make the iteration function about five times faster by compiling it. Here's the new version:

```cJulia =
Compile[{{c, _Complex}, {k, _Complex}},
-Length[
FixedPointList[#^2 + k &, c, 35, SameTest -> (Abs[#2] > 2.0&)]
]];

Show[
GraphicsArray[
Table[
ListDensityPlot[
Table[ cJulia[x + y I, a + b I],
{y, -1.1, 1.1, 0.0628}, {x, -1.1, 1.1, 0.0628}],
Mesh -> False, Frame -> False, Axes -> False,
AspectRatio -> 1, DisplayFunction -> Identity],
{b, -1.0, 1.0, 1/3.}, {a, -2.0, 1.0, 1/3.} ]]];
```

Designed and rendered using Mathematica versions 2.2 and 3.0 for the Apple Macintosh.