Monthly Archives

May 2007

Last Fractal

Photo of the Day

Ok, here’s a last fractal (for now). I’m just completing a set of fractal images for printing 6’x6′ (that’s big!) and will finish off this month’s blog by showing you just one more:

Detail within the Mandelbrot set fractal.  This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features.  Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself.  Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves.  Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns.  The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set, Mandelbrot set

Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set.
Image ID: 10376
Species: Mandelbrot Fractal, Mandelbrot set

Fractal of the Day

Photo of the Day

Whoa, here’s another crazy fractal from the Mandelbrot set. When I was setting the colors on this one it sort of reminded me of the trippy hippy art of the ’70’s. Right on man.

The Mandelbrot Fractal.  Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself.  Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves.  Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns.  The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set, Mandelbrot set

The Mandelbrot Fractal. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set.
Image ID: 18737
Species: Mandelbrot Fractal, Mandelbrot set

Fractal of the Day.

Mandelbrot Fractal Picture

Photo of the Day

Fractal ‘o’ the day, from the classic Mandelbrot family of inequalities:

Detail within the Mandelbrot set fractal.  This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features.  Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself.  Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves.  Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns.  The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set, Mandelbrot set

Detail within the Mandelbrot set fractal. This detail is found by zooming in on the overall Mandelbrot set image, finding edges and buds with interesting features. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set.
Image ID: 10378
Species: Mandelbrot Fractal, Mandelbrot set

More fractal pictures.

Julia Set Fractal

Photo of the Day

Today’s fractal picture is:

Fractal design.  Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself.  Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves.  Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns.  The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set, Mandelbrot set

Fractal design. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set.
Image ID: 18732
Species: Mandelbrot Fractal, Mandelbrot set

I think this one was generated with from the Julia set rather than the Mandelbrot set, but not 100% sure.

Fractal Picture

Photo of the Day

Here’s another example of detail within the Mandelbrot fractal set, illustrated by assigning color to the number of iterations required for the expression to explode:

The Mandelbrot Fractal.  Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself.  Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves.  Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns.  The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set, Mandelbrot set

The Mandelbrot Fractal. Fractals are complex geometric shapes that exhibit repeating patterns typified by self-similarity, or the tendency for the details of a shape to appear similar to the shape itself. Often these shapes resemble patterns occurring naturally in the physical world, such as spiraling leaves, seemingly random coastlines, erosion and liquid waves. Fractals are generated through surprisingly simple underlying mathematical expressions, producing subtle and surprising patterns. The basic iterative expression for the Mandelbrot set is z = z-squared + c, operating in the complex (real, imaginary) number set.
Image ID: 18729
Species: Mandelbrot Fractal, Mandelbrot set

Fractal pictures.

Photo of the Temple of Hatshepsut

Egypt, Photo of the Day

The Temple of Hatshepsut is the mortuary temple for Pharoah Hatshepsut, one of the rulers of the 18th Dynasty of ancient Egypt and one of the most successful female pharoahs in history. The Temple of Hatshepsut is located at Deir el-Bahri, near the Valley of the Kings, across the Nile River from Luxor, Egypt. The colonnaded Djeser-Djeseru building, shown here, lies at the foot of spectacular cliffs and is worth a visit when travelling in the Nile Valley.

Temple of Hatshepsut, Luxor, Egypt

Temple of Hatshepsut.
Image ID: 02588
Location: Luxor, Egypt

Photo of the Ramesseum

Egypt, Photo of the Day

The Ramesseum is the mortuary temple for one of the greatest rulers the world has ever known: Pharoah Ramesses II. Also known as Ramesses the Great, Ramesses II was a 19th Dynasty pharaoh who ruled for 67 years during the 13th century B.C. The Ramesseum is part of the ancient Theban necropolis, across the Nile from what is now Luxor, Egypt. The ironic sonnet Ozymandius aluded to Ramesses II.

Ramesseum, Luxor, Egypt

Ramesseum.
Image ID: 02586
Location: Luxor, Egypt

Ramesseum, Luxor, Egypt

Ramesseum.
Image ID: 02590
Location: Luxor, Egypt

Ramesseum photos.

Photo of the Borrego Badlands from Fonts Point

California, Desert

From Font’s Point in Anza-Borrego Desert State Park, one can look across the Borrego Badlands (Carrizo Badlands), once an ancient lake but now a corrugated, tortured, barren wasteland (e.g., Mordor).

Carrizo Badlands viewed from Fonts Point, Anza-Borrego Desert State Park, Anza Borrego, California

Carrizo Badlands viewed from Fonts Point.
Image ID: 05530
Location: Anza-Borrego Desert State Park, Anza Borrego, California, USA

Carrizo Badlands viewed from Fonts Point, Anza-Borrego Desert State Park, Anza Borrego, California

Carrizo Badlands viewed from Fonts Point.
Image ID: 05533
Location: Anza-Borrego Desert State Park, Anza Borrego, California, USA

Font’s Point photos, Anza-Borrego Desert State Park photos, Borrego Badlands photos, Carrizo Badlands.

Photo of 17 Palms Oasis

California, Desert

17 Palms Oasis is located in Anza-Borrego Desert State Park, several miles down the lunar-looking Arroyo Salado wash. The drive along Arroyo Salado is fun and relatively simple, although a four-wheel drive car is recommended. Seventeen Palms Oasis, consisting of (not surprisingly) 17 palms, appears out of nowhere as you drive down the wash and is a curious finding in the middle of such a barren landscape. It exists because of a shallow, subsurface supply of fresh water.

Seventeen Palms Oasis, Borrego Badlands, Anza-Borrego Desert State Park, Anza Borrego, California

Seventeen Palms Oasis, Borrego Badlands.
Image ID: 05538
Location: Anza-Borrego Desert State Park, Anza Borrego, California, USA

Seventeen Palms Oasis, Borrego Badlands, Anza-Borrego Desert State Park, Anza Borrego, California

Seventeen Palms Oasis, Borrego Badlands.
Image ID: 05539
Location: Anza-Borrego Desert State Park, Anza Borrego, California, USA

17 Palms Oasis photos, Seventeen Palms Oasis photos, Anza-Borrego Desert State Park photos.

Sunset Colors

Photo of the Day

Over the years I have had the good fortune to spend many weeks on liveaboard boats, in remote locations, diving and shooting photos. Typical trips will schedule some night dives, however we are not hard core on the diving and usually prefer to stay dry in favor of happy hour and an end-of-day skiff ride along the shore. Sunset on these trips is a golden time: gather on the sundeck, shake the last bits of seawater water out of the ears, enjoy one of Bob Heil’s blender concoctions and watch the sky light up.

Clouds and sunlight, La Jolla, California

Clouds and sunlight.
Image ID: 04817
Location: La Jolla, California, USA

Sunset and water, Sea of Cortez

Sunset and water, Sea of Cortez.
Image ID: 00285

Clouds and sunlight, Maui

Clouds and sunlight.
Image ID: 05642
Location: Maui, Hawaii, USA

Clouds at sunset, rich warm colors and patterns, Guadalupe Island (Isla Guadalupe)

Clouds at sunset, rich warm colors and patterns.
Image ID: 18514
Location: Guadalupe Island (Isla Guadalupe), Baja California, Mexico

Clouds at sunset, rich warm colors and patterns, San Clemente Island

Clouds at sunset, rich warm colors and patterns.
Image ID: 18515
Location: San Clemente Island, California, USA

Sky and cloud photos, sunset photos.