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At first, please look and read gBurning Birdh at the museum of mathematical science. If you say gWhat is a fractal? What is a Mandelbrot set?h, please see this page.

The Mandelbrot set is defined by the complex quadratic polynomial z = z^2 + c. If we take the absolute value of z under iteration, we can see, what is called, the gBurning Shiph .@ Furthermore if we take the absolute value of the only imaginary part of z, we can see the gBurning Birdh as the following images.

The main subject of my web pages is to be surprised like gWow! How cool!h. But we can get more mysterious factors from these images.

The following image is the overview of the gBurning Birdh.

The next image is one magnified with the red square area on the above image.

Please watch the domains around @AB, There are very complicated and unclear patterns. Magnifying the domains around @AB, then we can see more mysterious and interesting patterns than the well-known Mandelbrot set.

The left side domain evolves under the chaotic behavior. Around this area, the noises like the sand storm are only seen by any magnification (these may turn out to the one part of the gBurning Shiph). On the other hand, the right side domain is a fractal. The images and patterns are similar to the well-known Mandelbrot set. Now we pay attention to the domain between the chaotic domain and the fractal domain. The mysterious and interesting patterns may occur in this situation.

Furthermore we find the line-symmetric feature around here. This may one reason for the patterns similar to the living creatures (almost all the living creatures are line-symmetric).

The images below are the magnified ones around @AB excepting "Dancing Hobbit". There are just the portions of this exciting domain, you can find more! Here I only use very simple gradated colors from black to sky blue. It seems that this simple gradation brings out these beautiful scenes (more complicated gradations are popular, but it may kill this beauty).

We will be surprised at the magnified images and patterns, just like gWhat!? Ifve found the living creatures! They live!h

A lot of living creatures live and hide in the gBurning Birdh.

The following screenshots are just a part of them and their coordinates.

Reptiles with a mortarboard?
( -0.2315948126375350 +0.7081128782682475 i ) } ( 0.00000060212 +0.0000004816 i )
Crab in tears?
( -0.2309136545325250 +0.7187704924590650 i ) } ( 0.0000000055301 +0.000000004424 i )

( -0.2572407876501265 +0.7390125826886436 i ) } ( 0.000000000005484 +0.000000000004387 i )
( -0.2536823430193340 +0.7379389781045120 i ) } ( 0.000000000008277 +0.0000000000066220 i )

Lesser panda on the time machine?
( -0.2572404744012860 +0.7390129695766565 i ) } ( 0.0000000000004440 +0.0000000000003552 i )
Clay image of a man? Do not look at me!
( 0.2389388924017885 +0.5522564565853055 i ) } ( 0.0000000000064035 +0.000000000005122 i )

Man with a pointy hat?
( 0.2389769842158350 +0.5522292688468815 i ) } ( 0.0001477 +0.0001181 i )
United planarians?
( 0.2389395259018005 +0.5522594355655935 i ) } ( 0.000009364 +0.000007491 i )

What do you appeal to me?!
( -0.2315929166573230 +0.7081142803055840 i ) } ( 0.0000006511 +0.00000052093 i )
Dancing hobbit with bouquets?
( -0.1583692297789790 +0.6545039205714055 i ) } ( 0.00000000023095 +0.0000000001847 i )


This is software like a screen saver displaying these living creatures.


Please extract and execute this file, then you can randomly see the living creatures in the fractal world.
Putting ESC key on or clicking your mouse terminates this program.
Attention! This software consumes huge CPU resource. If your computer is over-clocked, please pay attention to gcomputer freezeh.

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