The Mandelbrot source can
be used to add a regular rectilinear grid with scalar values derived from
the Mandelbrot set to the 3D scene. The values in the grid are the number
of iterations it takes for the magnitude of the value to get over 2. The
equation repeated is z
= z2 + C (z
and C are complex). Initial
value of z is zero, the real value of C is mapped onto the x axis, and
the imaginary value of C is mapped onto the Y Axis. The third dimension
(z axis) is the imaginary value of the initial value. By default a two
dimensional data set is created with 251x251 values on the z=0 plane.
The size of the output data as well as the parameters for generating the
data can be controlled using the property sheet for the Mandelbrot source.
The output Mandelbrot image can be translated,
rotated, and scaled using the Actor control area of the Display tab for
this source, and it can be interactively positioned using the Move operation
of the camera. The
object created by this source is a vtkImageMandelbrotSource
object, and the output of this source is vtkImageData.
An example
of a Mandelbrot source is given on the right.
The Mandelbrot source has the following
parameters:
Extent:
These six values indicate the X, Y, and Z extent of the output data. The
first two numbers are the minimum and maximum X extent, the next two are
the minimum and maximum Y extent and the final two are the minimum and
maximum Z extent. The numbers are inclusive, so the default values of
0, 250, 0, 250, 0, 0 indicate that a single image of 251x251 values will
be created.
Sub-space:
These three values allow you to set the projection from the
4D space to the axes of the 3D Volume.
By default, the real component of C (represented by 0) is mapped to the
X axis, the imaginary component of C (represented by 1) is mapped to the
Y axis, and the real component of X (represented by 2) is mapped to the
Z axis. The imaginary component of X is represented by 3. All values entered
must be between 0 and 3 inclusive.
Origin:
The four values indicate the values of C (real and imaging) and the initial
value X (real and imaging). The first two number represent the real and
imaging components of C, with the last two indicating the real and imaging
components of X.
Size:
These four values indicate the four dimensional size of which to create
the output image.
Max
Iterations: This number indicates the maximum number of iterations
to perform in order to determine if the value will go above 2.
The Mandelbrot source can
be used to add a regular rectilinear grid with scalar values derived from
the Mandelbrot set to the 3D scene. The values in the grid are the number
of iterations it takes for the magnitude of the value to get over 2. The
equation repeated is z
= z2 + C (z
and C are complex). Initial
value of z is zero, the real value of C is mapped onto the x axis, and
the imaginary value of C is mapped onto the Y Axis. The third dimension
(z axis) is the imaginary value of the initial value. By default a two
dimensional data set is created with 251x251 values on the z=0 plane.
The size of the output data as well as the parameters for generating the
data can be controlled using the property sheet for the Mandelbrot source.
The output Mandelbrot image can be translated,
rotated, and scaled using the Actor control area of the Display tab for
this source, and it can be interactively positioned using the Move operation
of the camera. The
object created by this source is a vtkImageMandelbrotSource
object, and the output of this source is vtkImageData.
An example
of a Mandelbrot source is given on the right.