Monthly Archives

May 2007

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.
Image ID: 10376
Species: Mandelbrot Fractal, Mandelbrot set

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.
Image ID: 18737
Species: Mandelbrot Fractal, Mandelbrot set

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.
Image ID: 10378
Species: Mandelbrot Fractal, Mandelbrot set

More fractal pictures.

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.
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.

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.
Image ID: 18729
Species: Mandelbrot Fractal, Mandelbrot set

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.
Image ID: 02588
Location: Luxor, Egypt

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.
Image ID: 02586
Location: Luxor, Egypt

Ramesseum.
Image ID: 02590
Location: Luxor, Egypt

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.
Image ID: 05530
Location: Anza-Borrego Desert State Park, Anza Borrego, California, USA

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.

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.

Image ID: 05538
Location: Anza-Borrego Desert State Park, Anza Borrego, California, USA

Image ID: 05539
Location: Anza-Borrego Desert State Park, Anza Borrego, California, USA

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.
Image ID: 04817
Location: La Jolla, California, USA

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

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

Clouds at sunset, rich warm colors and patterns.
Image ID: 18514