Last Update May 1, 2004 　日本語はこちら

#### NUMERICAL SPACE / MANDELBROT_FRACTAL

Recent fractal galleries show so splendid images from excellent softwares. They are depending on the newest powerful personal computers. For this, I remember that I had been making fractal images by my expensive primitive personal computer and BASIC programs I typewote. I had got a simple fractal after several hours with a high excitement.
This time I played fractals by those classic and simple logics on the book, written by Ms. Kiyoe Fuchigami and published in 1987.
How about fractals? Let's enjoy them.

News! Mr. Shinichiro started a new web site for Mandelbrot fractal. There are many simple but beautiful Mandelbrot fractal images on this page. He opened their scene files to the public as Mset_DEM_en.zip(5 kB).

 A image like "terraced fields". This is called as "Self Square Fractal" and got from the repeated times (I used 0.2th power of the times value.) of "zn+1 = f(zn)" on the function below on complex coordinates to rise up over some value.f(z) = z*z +1.5+2.2i I applied POV's "smooth_triangle" and colored it from red to white by "gradient color_map". Scene file : lpmdterc.txt

Terraced Fields / 43k / Sept. 2000 / by Tsutomu Higo

 A image like "whirls". This is a same sort of fractal with upper. The function is as follows. f(z) = z*z -0.76+0.2i I applied POV's "smooth_triangle" and colored it from blue to white by "gradient color_map". Scene file : lpmduzup.txt

Whirl_Plate / 53k / Sept. 2000 / by Tsutomu Higo

 This is just same with upper and I used frames for expressing the image. Scene file : lpmduzuf.txt

Whirl_Frame / 98k / Sept. 2000 / by Tsutomu Higo

 This is just same with upper 2 and used sheres for expressing the image. Scene file : lpmduzus.txt

Whirl_Sphere / 77k / Sept. 2000 / by Tsutomu Higo

 This is called as "Mandelbrot Set" and got from the repeated times (I used 0.1th power of the times value.) of "zn+1 = fc(zn)" (The initial value of z is 0.) on the function below on complex number C of some complex coordinates area to rise up over some value. fc(z) = z*z +CI applied POV's "smooth_triangle" and colored it from red to pink by "gradient color_map". Scene file : lpmdl1.txt

Mandelbrot Mountain / 28k / Sept. 2000 / by Tsutomu Higo

 This is almost same with upper. I used the function below. The figure of Mandelbrot set has some knots like this. The number of knots is power number of "z" -1. So this image has "4 -1 = 3" knots.fc(z) = z4 +CI applied POV's "smooth_triangle" and colored it from blue to white and gray top by "gradient color_map". Scene file : lpmdl3.txt

3 Directions Mandelbrot Mountain / 25k / Sept. 2000 / by Tsutomu Higo