|
|
|
Picture 1: Ingvar kullberg: Natural Minibrot |
Picture 2: A MiniJulia derived from the left minibrot. |
| . . . |
Spot Light Corner: Ingvar's method to turn a "regular" Minibrot into a MiniJulia? It all started as we were busy exploring various minibrot forms, searching especially bizarre shapes for a list challenge. Many beautiful and bizarre creatures were produced, when Stig has come out with a new discovery: a minibrot with the form of a Julia instead of a Mandelbrot. This strange creature has aroused immediately the curiosity of all. Stig originated his MiniJulia from a perturbed M set. Later Ingvar has deducted, "that the Julia structure of the perturbed M set is clearly situated in the head of the non-perturbed M set." Well, soon enough Ingvar, the classic-Mandel master, has come up with a new and simple method to create this amazing MiniJulias. I will let Ingvar explain it with his own words: Hi all fractal artists, The M set (the Mandelbrot) resides on the parameter plane (c_real, c_imag) while the Julias on the dynamical plane (z_real, z_imag), that is the plane where the iteration takes place. It showed up that MiniJulia images may be originated from the perturbed M set. A similar image *could* have been produced in the following way: 1) Choose a minibrot. For the example. let's take the minibrot in picture 1 above. 2) Use the "Switch Julia" icon and click a parameter value from the head of this minibrot. A Julia fractal will appear in a new popup window (picture 3). Important: You must turn the period check off, otherwise artifacts will appear. You must also increase the iteration number to match the same value as used for the minibrot.  Picture 3: The Julia fractal created by the Julia Switch. 3) Zoom in to the center of this Julia, again and again, and after a while a "MiniJulia" (picture 2) will appear, which has the same type of environment as the minibrot. To extend the similarity you will have to copy and paste the gradient of the minibrot onto the gradient of the MiniJulia. I would like to add, that as the parameter is taken from the M set, the Julia set is connected, and the critical point, z = 0, belongs to the filled-in Julia set (the Julia set plus eventually enclosed regions). God luck!!! Here are the parameters for the Minibrot and the MiniJulia:
Mini2 {
fractal:
title="Mini2" width=640 height=480 numlayers=1
layer:
caption="Layer 1" visible=yes alpha=no
mapping:
center=-1.758328866413543/0.0120548774690095764 magn=74336344752.4356064
angle=0
formula:
filename="Standard.ufm" entry="FastMandel" maxiter=50000 percheck=normal
p_Start=0/0 p_Bailout=100
inside:
transfer=none repeat=yes
outside:
density=0.5 transfer=linear repeat=yes
gradient:
smooth=yes numnodes=7 index=3 color=0 index=27 color=65530 index=83
color=329215 index=141 color=15335546 index=210 color=32 index=332
color=17749 index=372 color=62720
}
Regards,Ingvar |
|
|
| Picture 4: Classic Minibrot | Picture 5: Classic Minibrot |