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 数理科学美術館　 「 燃える鳥 」　( ＝ Burning Bird ) Created at the Spring 2009 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 non-bounded values, then we can see colorful images of the Mandelbrot set. You may have seen the images similar to this. Recently I heard the “Burning Ship Fractal”. If we take the absolute value of z under iteration, we can see the image like the ship burning down. This is called the “Burning Ship”. The following one is an overview of the “Burning Ship” (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 non-bounded values, we may find out a ship burning down. The “Burning Ship” 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 “Burning Ship”. We can see the flame on the ship taking the shape of some artificial structure like a tower. I’ve made high-quality 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...    Don’t 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 “Burning Bird”. I’ve also made high-quality images for the desktop wallpaper, see the link located below. We may have more variation on the magnified images of the “Burning Bird” than the ones of the Mandelbrot set or the “Burning Ship”. The followings are the magnified images of the “Burning Bird”, “Burning Ship” 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, isn’t 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 low-gradated images appear). I draw these images with the alternated version of this.
( Resolution of all the images is 3840x2400 WQUXGA)
※You may use these with resolution of 1920x1200 or 2560x1600    ```Type= Mandelbrot Set AreaS= -3.000 -1.875 i AreaE= +3.000 +1.875 i Color= 5 0 1 ``` ```Type= Burning Ship AreaS= -1.86359 -0.10405 i AreaE= -1.645120 +0.03249 i Color= 1 0 0 ``` ```Type= Burning Bird AreaS= -0.789602 +0.921586 i AreaE= -0.781340 +0.926750 i Color= 1 0 0 ``` ```Type= Burning Ship AreaS= -1.7541100 -0.0244705 i AreaE= -1.7523500 -0.0233705 i Color= 7 0 1 ```    ```Type= Burning Bird AreaS= -1.343353032 +0.052243724 i AreaE= -1.343335300 +0.052254806 i Color= 7 0 1 ``` ```Type= Burning Bird AreaS= -1.343353032 +0.052243724 i AreaE= -1.343335300 +0.052254806 i Color= 0 0 0 ``` ```Type= Burning Bird AreaS= -1.3592307029885 +0.0460937308951 i AreaE= -1.3592307021130 +0.0460937314423 i Color= 1 0 0 ``` ```Type= Burning Bird AreaS= -1.3592307029885 +0.0460937308951 i AreaE= -1.3592307021130 +0.0460937314423 i Color= 0 0 0 ```    ```Type= Burning Bird AreaS= -1.3592307029885 +0.0460937308951 i AreaE= -1.3592307021130 +0.0460937314423 i Color= 4 0 1 ``` ```Type= Burning Bird AreaS= -0.9987323900383 +0.5360573078211 i AreaE= -0.9987323885626 +0.5360573087434 i Color= 4 0 1 ``` ```Type= Burning Bird AreaS= -0.9987323900383 +0.5360573078211 i AreaE= -0.9987323885626 +0.5360573087434 i Color= 4 0 0 ``` ```Type= Burning Bird AreaS= -1.3433433990 +0.0522457171 i AreaE= -1.3433406890 +0.0522474109 i Color= 0 0 0 ```    ```Type= Burning Bird AreaS= -1.0349 +0.5732 i AreaE= -0.3418 +1.0063 i Color= 2 0 0 ``` ```Type= Burning Bird AreaS= -0.842966323693 +0.696088439537 i AreaE= -0.842966308803 +0.696088448843 i Color= 3 0 0 ``` ```Type= Burning Bird AreaS= +1.04567571364 -1.09543453020 i AreaE= +1.04567578488 -1.09543448567 i Color= 0 0 1 ``` ```Type= Burning Bird AreaS= -0.785947828880 +0.924588685095 i AreaE= -0.785947816488 +0.924588692840 i Color= 0 0 1 ```    ```Type= Burning Bird AreaS= -0.785947829591 +0.924588684120 i AreaE= -0.785947815305 +0.924588693049 i Color= 4 0 0 ``` ```Type= Burning Bird AreaS= -0.9987342450 +0.5360569901 i AreaE= -0.9987309220 +0.5360590669 i Color= 2 0 0 ``` ```Type= Burning Bird AreaS= -1.74725850 -0.00213317 i AreaE= -1.74702064 -0.00198451 i Color= 3 0 0 ``` ```Type= Burning Bird AreaS= +1.03855533 -1.16894307 i AreaE= +1.03870251 -1.16885109 i Color= 7 0 1 ```    ```Type= Burning Bird AreaS= +1.036478 -1.169717 i AreaE= +1.041227 -1.166748 i Color= 7 0 0 ``` ```Type= Burning Bird AreaS= -0.785947824055 +0.924588676100 i AreaE= -0.785947809404 +0.924588685257 i Color= 7 0 1 ``` ```Type= Burning Bird AreaS= -1.3649939773416500 +0.0762914164832801 i AreaE= -1.3649939773391799 +0.0762914164848239 i Color= 0 0 0 ``` ```Type= Burning Bird AreaS= -1.364993977351950 +0.076291416477686 i AreaE= -1.364993977330640 +0.076291416491004 i Color= 1 0 0 ```    ```Type= Burning Bird AreaS= -0.785816564 +0.924787018 i AreaE= -0.785799450 +0.924797714 i Color= 0 1 0 ``` ```Type= Burning Bird AreaS= -0.86053 -0.12630 i AreaE= -0.80310 -0.09041 i Color= 1 0 0 ``` ```Type= Burning Bird AreaS= -0.854259 -0.105743 i AreaE= -0.838559 -0.095931 i Color= 2 1 0 ``` ```Type= Burning Bird AreaS= -1.401213682 -0.000000731 i AreaE= -1.401208180 +0.000002708 i Color= 6 0 0 ```    ```Type= Burning Bird AreaS= -1.4012082250 +0.0000014414 i AreaE= -1.4012073096 +0.0000020135 i Color= 6 0 0 ``` ```Type= Burning Bird AreaS= -0.2340910 +0.7075123 i AreaE= -0.2317252 +0.7089909 i Color= 0 0 0 ``` ```Type= Burning Bird AreaS= -0.2318859 +0.7078198 i AreaE= -0.2313917 +0.7081287 i Color= 0 0 0 ``` ```Type= Burning Bird AreaS= -0.23174455 +0.70801852 i AreaE= -0.23153883 +0.70814710 i Color= 0 0 0 ```    ```Type= Burning Bird AreaS= -0.231599784 +0.708109755 i AreaE= -0.231587288 +0.708117565 i Color= 0 0 0 ``` ```Type= Burning Bird AreaS= -0.2315942857 +0.7081132827 i AreaE= -0.2315915874 +0.7081149691 i Color= 0 0 0 ``` ```Type= Burning Bird AreaS= -0.2315937599 +0.7081137336 i AreaE= -0.2315920877 +0.7081147787 i Color= 7 0 0 ``` ```Type= Burning Bird AreaS= -1.4008658938343 +0.0004420602912 i AreaE= -1.4008658911399 +0.0004420619753 i Color= 1 0 0 ```

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