Mirage in the Painted Desert
Fractal Art Main Gallery

Every fractal image in this gallery was generated by iterating a single dynamical system such as the Mandelbrot equation zn+1 = zn2 + p strictly following the basic methods illustrated by Stories about Fractal Plotting and without using extra graphical manipulations (such as pasting two or more images) made available by graphics software. For example, in "Mirage" above, the mountains beyond certain distance were altered to clouds by simply changing the coloring scheme. It is generated by the logistic equation zn+1 = p(1 - zn) zn. The exciting element of fractal plotting is to unearth beautiful, curious, strange or startling images hidden in an equation. More advanced 3D fractal images such as realistic fractal mountains with natural shadings are shown in the Fractal Art Gallery Annex.

Click on any of the pictures below to see a larger version or a group of pictures having the same motif. Some of the pictures accompany technical descriptions that make reproductions possible. It is interesting to note, however, that because of the chaotic nature inherent to nonlinear equations, fractal images are somewhat computer-dependent. So, don't be alarmed if you try it out using your newest machine/compiler that utilizes higher-precision numbers and don't get exactly the same pattern.

Fatou and Julia Patterns
Phoenix I
Phoenix II
Logistic Equation
Logistic Elephants
Balancing Elephants
Jumping Elephant
Running Elephant
Logistic M Set
Lightning M Set
Elephant Wallpaper
Centipede Maze
Centipede Maze
Four Seasons
Spring Reflection
Cool Summer
Early Autumn
Golden Autumn
Winter Night
The M Set
Rotated Plate
Deformed Plate
Broken Plate
M Set Spotted
Cuttlefish Party
Pansies
Cosmos
Daisy
Dancing Beans
Caterpillar
Julia Dragons
Elephant Seahorses
Dancing Seahorses
Dancing Seahorses
Goldfish in Love
Moray Eel
Jellyfish Family
Newton Patterns
Newton's Basins
5th Roots of Unity
8th Deg Flowers
11th Deg Flowers
Fireflies
Tamarack Lake
Octopus Family
Barn Owl
Dragonfly
Dragonfly Party
12th Deg Spiders
20th Deg Spiders
Bee Garden
15th Deg Garden
20th Deg Garden
Butterfly Garden
Newton Ferns
Butterfly Pebbles
Crab Family
Dancing Julia Set
Crab Family II
Bronze Age God
Bubo
Mythical Animal
3D Fractals by Basic Method
Crevasses
Lake
Chinese Mist
Japanese Wind
American West
South Pole
Go to Sekino's Fractal Home Fractal Art Gallery Annex Stories about Fractal Plotting and Fractal Art