Douady's Rabbit Flower



http://www.fractalforums.com/index.php?action=gallery;sa=view;id=352

Another tribute to Adrien Douady, who passed away in 2008. Adrien Douady  was a French Mathematician and fractal pioneer. This image features a "Douady's Rabbit" figure in it's center. A Douady's Rabbit is a Julia set plot that has pairs of buds on it that look like a rabbit's ears.

The plot is from a tendril coming from the spiral of an "<b><u><a href="http://www.pbase.com/duncanc/image/83612942">elephant</a></u></b>" in "<b><u><a href="http://www.pbase.com/duncanc/image/79579853">Elephant Valley</a></u></b>" of the largest baby Mandelbrot on the real axis. It's taken from a baby Mandelbrot on the tendril.

The plot uses distance estimate data to calculate a height value for each point. It's plotted with exaggerated height values from a very close point of view. The close point of view creates perspective distortion that makes the "petals" of the flower look like they are radiating from the center of the image.

The details of the plot are as follows:

Document name:   Douady's rabbit flower.FWrk
Fractal type:   julia
Plot size (w,h):   1200,   1200
Maximum iterations:   10000
Center Point (real, imaginary):   -1.747808276,   -0.001644990015 i
Plot Width (real):   8E-09
Julia origin (real, imaginary):   -1.747808277001616,   -0.001644989673806953 i
Source mandelbrot width:   2.5E-09

Color scheme name:   Clematis colors
Color scheme last modified:   2008-08-14 18:04:00 -0400
Plot uses DE:   Yes
Plot uses fractaional iterations:   Yes
Plot height:   1
Peak steepness:   1
Plot flipped:   Yes
Camera x:   0
Camera y:   0
Camera z:   -2.05
Ambient light:   0.2
Directional light:   0.6
Specular light:   0.2
Surface shininess:   100
Light x direction:   -1
Light Y direction:   1
Light z direction:   1
Background color red:    75
Background color green:    83
Background color blue:    63

If you have a recent version of FractalWorks you can recreate this plot on your Macintosh by clicking the link below:

<u><a href="fractalworks://x?type=julia&plot_height=1200&plot_width=1200&max_iterations=10000&center_r=-1.747808276&center_i=-0.001644990015&r_width=8E-09&c_real=-1.747808277001616&c_imag=-0.001644989673806953&sourcemandelmagnification=2.5E-09&calc_de=y&calc_frac=y&colorscheme=Clematis%20colors&color_info=un=255/255/255,set=226/45/24,use_de=n,use_frac_smooth=y,band=c_type=1;adj=0.0001;a_type=1;a_val=1;g_type=1;steps=1;spacing=1;phase=0;s_rgb=76/178/37;e_rgb=107/150/58,band=c_type=1;adj=0.9221;a_type=2;a_val=0.35;g_type=1;steps=1;spacing=1;phase=0;s_rgb=107/150/58;e_rgb=95/30/174,band=c_type=1;adj=0.3248;a_type=2;a_val=0.46;g_type=1;steps=1;spacing=1;phase=0;s_rgb=95/30/174;e_rgb=200/209/255,band=c_type=1;adj=0.0001;a_type=2;a_val=0.7701;g_type=1;steps=1;spacing=1;phase=0;s_rgb=200/209/255;e_rgb=161/159/42,band=c_type=1;adj=0.0001;a_type=2;a_val=0.8811;g_type=1;steps=1;spacing=1;phase=0;s_rgb=161/159/42;e_rgb=206/206/89&">Fractalworks plot Douady's rabbit flower</a></u>