FOTD -- February 05, 2009 (Rating 8) Fractal visionaries and enthusiasts: The question of fractal reality sometimes arises to puzzle even the most devoted fractal fans, and sooner or later every fractal fan asks himself, "Are fractals real?" To begin, fractals must have some kind of reality. How else could we have pictures and animations of them? But it is obvious that fractals are not made of material. They appear to be more like mathematical abstractions, but abstractions have no shape, so how can fractals be abstractions? Mathematics is basically human thought processes stated in symbolic form, so could fractals be made of thought? Thoughts are usually considered to be less real than objective material objects. This is why we say, "ghosts are not real, they exist only in the mind." But sometimes thoughts can become almost real. In dreams, for instance, thoughts can appear quite as objectively real as any material object. So are fractals made of semi-materialised thought? If fractals are made of thought, we then wonder what thought is made of? A materialist would claim that thought is a by-product of the brain. So if fractals are made of thought, they are therefore created by the neural activity of the brain. But what is neural activity? Cognitive specialists tell us that neural activity consists mainly of electric and chemical interactions between neurons. Now it looks like fractals are made of electro- chemical interactions. I could continue by asking what are the interactions made of, but an endless regression is now becoming apparent. At the same time, an idealist, such as myself, would tell us that with thought we have reached the end of the line. Con- scious thought is the ultimate reality, and it is meaningless to ask what thought is made of. My conclusion is that fractals are made of thought, which can take many forms from total abstrac- tion to a rock-solid impression of objective material reality. Fractals are quite real, in fact they are as real as thought. Now let's end the philosophical fractal digression and say a few words about today's image. I named the image "Venusian Landscape" because something about it reminds me of the first pictures sent back from the surface of Venus. I rated it at an 8 because, unlike the surface of that planet, the image has a rather sunny feeling about it. The parent fractal is a cubic Mandelbrot set surrounded by seven spokes inside a circle that makes the set resemble the hub of a wheel. Today's image is located some distance to the northeast of the cubic Mandeloid. The calculation time of a zippy 1-1/4 minutes should bring happiness to every fractalist. Hard-to-please fractalists may find comfort on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image is posted for instant viewing. Lots of sun prevailed here at Fractal Central on Wednesday, though a morning low of 16F -9C made for quite a chilly start to the day. The high of 28F -2C was a little better. The fractal cats thoroughly enjoyed the sun. With the main computer back and up and running, my day was fair enough. The next FOTD will be posted in 24 hours. Until then, take care, and is the mind a by-product of the brain or are the things we call brains actually sense-produced images in the mind? Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Venusian_Landscape { ; time=0:01:13.55-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot6 logmap=67 periodicity=10 center-mag=+0.9168008632085998/+1.217061671902639/\ 6.61573e+010/1/170.5/0 params=-6/11/0.001/0 float=y maxiter=1500 inside=0 passes=1 mathtolerance=0.05/1 colors=000_ZOkcPssMztJceGcZDcSBUL8UE5U72DzT6SEzi2j\ _1ZR1NI0B90czzRU0351230110nqzWXpOObGGQ88DunAlf8d_7\ XT5OL4GE2871wM6aH4SD3ZU9aOIwIRhCZfCddCjbCpaCubGscK\ qdNodRmeUkfYif`g`biWckQdmLeoGfqDXcANQ7ECJL9UR6dX3P\ eNAnfeFO`JMXNKSQIOUGKYEF`CBdA7g9BZJFQTIHaJIZJIWJJT\ JJQKJNKKKKKHKKFEPO8TX2Xe4`e5de6he7ke8oe9seAveJmVSd\ K_XAXSGUNMRISODYM8cPEmRKwNHsKFoHClEAhB7e85a53ZXSdx\ pjrekmVlgLlbAmY0mRGaLVQFiE9x2IvHRuWVnRZgNbaJeVEWBk\ VAjUAiTAiSAhR9gQ9fQ9eP9dO9dN8cM8bL8aK8`K7`J7_I7ZH7\ YG6XF6XE6WE6VD6UC5TB5SA5S95R84Q84P74O6Uz5UzmUz3Uz2\ UzmUz2Uz3UzmUz4Uz5UzmUz6UzmUz7UzmUz9czzczAczzczBcz\ zczDczzczEczzczFczzczGczzczIczzczzm7zz7zm6zz6zm5zz\ 5zm4zz4zm3zz3zm3zz4zm4zz4zm5zz5zw5zw5zw6zw6zw6zw6z\ w7zw7zw7zw7zw8zw8zw8zw8zw9zw9zw9zwAzwAzwAzwAzwBzwB\ zwBzwBzwCzwCzwCzwCzwDzwDzwDzzDzzEzzEzzEzzEzzDzzDzz\ DzzCzzCzzCzzCzzBzzBzzBzzB } frm:DivideBrot6 { ; Jim Muth z=(0,0), c=pixel, a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=z^(a)/(z^(-b)+d)+c |z| < f } END PARAMETER FILE=========================================