right, you as fractalist should be aware of that "new" sometimes just means the same structure "new" arranged, either rotated, multiplied or something
nevertheless, the deep explorers, like kalle reveal the "new" experience for an ongoing amount of fractals that offer their beauty just far below in the ultra deep regions as you all might experience right now
what i personally find new and very interesting is the shape stacking, i wonder if that can be used to reveal something really worthfull
so, what about a true challenge for shaped stacks that really form the whole alphabet ? isnt that possible right now to actually construct those?
I have a bit of experience with shape stacking, obviously.
http://stardust4ever.deviantart.com/art/Magnum-Opus-Ex-3132-6-Zooms-274474754With Mandelbrot, it is pretty strait forward. You find an interesting feature you want to double, so you select and inflection point within that feature. Zoom into the inflection point, to a spot approximately 50% deeper in zoom depth, and you will find your original feature neatly wrapped around the inflection point you chose, twice. In the 3rd order Mandelbrot, you pick a feature, find an inflection point not at the centroid, and zoom 33% deeper to find the original feature wrapped thrice around your chosen inflection point. Only in 2nd order Mandelbrot is it possible to line features up in neat concentric little rows.
Shape stacking operates a bit differently in formula which utilize an abs() function. Think of the ABS as a mirror. If you abs() the real value, the fractal gets reflected across the Y axis. If you abs() the imaginary value, the fractal gets reflected across the X axis. Shape stacking does work in the abs() variants, but it is not quite as trivial as with Mandelbrots.
Start with an interesting area within the Burning Ship. Pick a place you would like to replicate. Assuming the fractal is rendered so that the masts point up, when you decide upon an inflection point to zoom into, imagine a horizontal mirror being placed along that point, creating a line. Everything below that line gets reflected from the bottom half onto the top half. Then the half image is compressed to fit one fourth of the pie, and what you get is a periodic doubling with half of the information deleted, the remaining half reflected, then compressed and replicated by a factor of 2. For burning Ship, the plane of reflection is horizontal and zooming above the feature will create a more intricate pattern while zooming below the feature will create a less intricate pattern. Celtic fractals work the same way but the plane of reflection is vertical instead of horizontal. Remember, Celtic abs() the real side, Burning Ship abs() the imaginary side.
In the Buffalo Fractal, there are two planes of symmetry, so one quadrant gets reflected both ways by a factor of 4, and compressed and replicated by a factor of 2. The following image "Nuclear Clover" was generated by pattern stacking within the Buffalo set:
http://stardust4ever.deviantart.com/art/Nuclear-Clover-372268536Here's a visual example of what I'm talking about:
Zooming into the 8 circles along the outer rim of the source image within the Buffalo fractal will produce different fractal results when using pattern stacking method. Only by zooming into the circles in the upper left quadrant, is the centroid of the original image duplicated. For Burning ship with masts pointing up, zooming into the top of the pattern creates more detail. For Celtic with needle facing left, zooming into the left side of the pattern creates more detail. For Buffalo, zooming into the quadrant above the needle generates increasing detail. Other fractals you will have to experiment.
And I'm only just beginning to learn the hidden nuances in the 3rd order fractals so far. The 3rd order Burning Ship tends to create first twofold and then six-fold symmetry with snowflake-like patterns. Remember, in third order pattern stacking, you are taking a pattern, reflecting one half while discarding the other, and compressing the result by a factor of three. this creates the beautiful six-sided snowflake designs found within the 3rd Order Burning Ship. One cool thing about 3rd order is you don't have to zoom quite as deep as 2nd to replicate stuff.
March 21, 2008, 05:22:42 PM
3D burning ship
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