The gallery comprises fractal images that can be plotted on a plane by standard programming routines described in Stories about Fractal Plotting. We classify the images into four 
§ 2.
Logistic Equation and Other Dynamical Systems


The picture shown above is a "global" image generated by the logistic equation, which was created to model population dynamics. The equation was suddenly under the spotlight in the 1970s when its "chaotic" behavior was discovered and triggered the "Chaos Theory" to develop in mathematics. We can apply the logistic equation just like the Mandelbrot equation to find numerous fractal images.
The first five images shown below are given by zooming in on the vicinity of the righthand "antenna" of the global image, where the first sign of chaos was spotted in 1974. 

The image may be mapped onto: 







If we zoom in on the midpoint between each pair of eyes in "Jumping Elephants," we find a "snowman" figure (a replica of the M set) and one of them is shown below. As we shall see, the "snowman" figure pops up frequently in many dynamical systems. 

And here is a "branch" from the M set. 



In the global image of the third degree equation shown above at left, two "snowmen" are visible: One is shot by a Stone Age arrowhead and the other is the tiny figure on the right, whose magnified image is shown separately at right. Here are two scenes from the boundary of the tiny snowman: 


We often use the above image on the left as a night sky in 3D landscapes such as the one shown below. We show more 3D images in Gallery II. 



There are infinitely many dynamical systems for us to play with and each one of them generates a unique "global" shape like the ones shown above. For example, the first image is given by




