”—‰ÈŠw”üpŠÙ@ u ”R‚¦‚é’¹ v@( Burning Bird )
Environment: homebuilt computer with Core2Duo Language; Visual C++ 6
The following is the image of the Mandelbrot set which is graphed by the computer. We define the Mandelbrot set as the set of complex values of c for which the orbit of 0 under iteration of the complex quadratic polynomial z = z^2 + c remains bounded. Assigning black color for the bounded values and the other colors for the number of executed iterations at the nonbounded values, then we can see colorful images of the Mandelbrot set. You may have seen the images similar to this. Recently I heard the gBurning Ship Fractalh. If we take the absolute value of z under iteration, we can see the image like the ship burning down. This is called the gBurning Shiph. The following one is an overview of the gBurning Shiph (I put this image upside down).
The bounded values are painted by black color on this image. We may find this domain like the ship driving from the front. Furthermore assigning the red color for the nonbounded values, we may find out a ship burning down. The gBurning Shiph is also known by the following ones, which are magnified with the gray square area on the above image
Now magnifying the gray square area again, we can see the following one.
This may be the most popular image of the gBurning Shiph. We can see the flame on the ship taking the shape of some artificial structure like a tower. Ifve made highquality images for the desktop wallpaper, see the link located below. Now taking the absolute value of the only imaginary part of z under iteration, the completely different images appear.
Magnifying the gray square area, we can see the mysterious and interesting images. Please watch followings.
Magnifying the gray square area again and again...
Donft you find this like the phoenix? This is not like a roast chicken on the well known image of the Mandelbrot set. Yes, this is the gBurning Birdh. Ifve also made highquality images for the desktop wallpaper, see the link located below.
We may have more variation on the magnified images of the gBurning Birdh than the ones of the Mandelbrot set or the gBurning Shiph. The followings are the magnified images of the gBurning Birdh, gBurning Shiph and the Mandelbrot set. Only with the simple gradation and computed values, these intriguing images appear naturally.
Is it is interesting and amazing that the purely mathematical subjects turn out to the living creatures, artificial structures, bacteria, machines, starlit sky and so on, isnft it? As you see, there are the chaotic domain and the fractal domain with some magnification. At the chaotic domain, we can never find out any order like a logistic function (the spotted and lowgradated images appear).

Living creatures in the fractal world.
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