FOTD -- May 22, 1016 (Rating A-7,M-7)

Fractal visionaries and enthusiasts:

Today's image shows a scene in the parent fractal that results when Z^(2) and Z^(-1) are blended. Since there is no such thing as a minibrot of a negative unity order, (it would have negative-two main bays), all minibrots reach a floor at the quadratic level, with one lobe.

Today's minibrot did its best to be impressive, but I had to add some Fractint special effects to bring it up to FOTX worthiness. Rendering the image with the inside set to 'bof60' and the outside set to 'fmod' gave it just enough bells and whistles to make it worth being declared FOTX for May 22.

The reason for the name "MothEaten Minibrot" will become clear when the three minute parameter file is run in Fractint. The next FOTD, which very possibly might be posted in two days or sooner, will feature a fractal between quadratic and cubic that has no discontinuities and has enough zooms to make the most dedicated fan of zooming leap for joy.

It rained almost all day here at Fractal Central today, forcing myself and FL to spend the day indoors with the fractal cats. Until next time, take care, and trying to squeeze the quantum world into the world of classic Newtonian common sense is as futile as trying to squeeze a 4-dimensional hypercube into the 3-dimensional world without distorting it. Yet this is what the different interpretations of QM are apparently trying to do.

Jim Muth jimmuth@earthlink.net

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FOTD -- May 19, 2016 (Rating A-7,M-8)

Fractal visionaries and enthusiasts:

Today's image shows a little of what can be done with minibrots of the seventh order when they are calculated in a new way. The formula will reveal the new way, which I discovered several years ago while making up new random formulas, most of which drew beautiful blank screens.

When fractals go above the quintic level, they quickly begin to all look the same, and by the time we reach the tenth order, the difference between orders is hard to notice. But look at what lurks in fractals of the seventh order, (and higher orders as well), when we do something new with them. Not only do we have a near perfect minibrot, but there is a very interesting extended pattern surrounding it, partly derived from the parent quadratic Mandelbrot set.

This opens an entire new world of fractal exploration, at least for those who seek minibrots. It is also possible to have fractals of fractional orders without those annoying discontinuities, as well as fractals of negative orders. I have just recently begun exploring this stuff, and I'm sure I'll find more new discoveries, not only with today's formula, but with several new formulas I am working on, but have not yet worked the bugs out of.

It's such a pleasant day here at FC that I will skip my regular comments about controversial things and enjoy the final rays of sunshine along with FL and the fractal cats.

Today turned out quite pleasant here at Fractal Central, with partly cloudy skies, a temperature of 72F 22C, and sunshine that was brilliant between the clouds. The fractal cats took full advantage of the weather by sleeping through the afternoon, while FL puttered in her garden and I searched the internet for things of interest, which there is no shortage of. The next FOTD will be posted in the not too distant future. Until then, take care, and eventually righteousness will prevail, but how will we recognize it when it does?

Jim Muth jimmuth@earthlink.net

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FOTX -- May 18, 2016 (Rating A-7,M-6)

Fractal visionaries and enthusiasts:

Today's formula, the MandelbrotMix3 is about eight years old and mixes four different powers of Z into one hopefully superb fractal. I rarely use it because it requires the critical points to be calculated by hand. In today's image we mix Z^(1.8), Z^(-0.8), (Z), and Z^(+0.8). This unlikely mixture creates a parent fractal that at first glance appears to have little promise. And to make matters worse, we check one of the least promising areas. But fractals hold no end of surprises and today's image shows what sometimes lurks in the depths of fractals that appear dead on the surface.

No one was more surprised than myself when a universe filled with floating eggs appeared as I rotated the color palette. I immediately named the image "Quantum Egg World". I am currently quite interested in the debates going on in the field of quantum mechanics. Quantum stuff is also quite trendy among the general population. No one knows exactly what quantum theory is, but judging by how the word is so carelessly tossed about, the general feeling is that it must be something almost magical.

I'll have much more to say about the quantum conclusions I have arrived at over the past 15 months or so. Like everyone else, I will have no proof for any of the sometimes outrageous things I might say, but then, I will merely be expressing my personal opinions, not trying to convert anyone to mysticism or fight the rise of irrationality. The only thing I am now absolutely certain of is that if someone wants to know more about quantum theory, they should check something like 'quantum decoherence' on the internet. They will come away knowing even less than before they checked.

It was another overcast day here at Fractal Central. The high temperature of 64F 18C was well below the average high of 77F 25C. The fractal cats complained when I offered them a can of quantum cat food, which turned out to be both empty and filled at the same time. FL is getting impatient with the continued chilly, damp weather, which is slowing the growth of her flowers. The next FOTX will be posted in a few days. The FOTX artistic quality will be going up in a few days (I hope!). Until next time, take care and be happy with things the way they are.

Jim Muth jimmuth@earthlink.net

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FOTD -- May 16, 2016 (Rating A-7,M-9)

Fractal visionaries and enthusiasts:

Today's image is strange. The strangeness does not appear on the surface, which is a simple image of the large minibrot on the main stem of the Mandelbrot set. But do not yet give up hope. To see something strange indeed, check the obvious minibrot at the top center edge of the frame, on the filament extending from the northern bud of the large minibrot.

What is this we find?! An order 7 minibrot with quadratic surroundings!?

Assuming that you have already seen the mysterious 'brot, how is it possible? The minibrot is of order 7, nothing at all like the quadratic minibrot from which its filament extends. In fact, everything deeper in the same parent fractal is of order 7, while everything closer to the surface has a quadratic nature. The formula does it all.

As an extra surprise, raise the already huge imag(p1) parameter a few orders of magnitude and watch the order 7 minibrot gradually morph into a quadratic one.

Another bonus with this formula, which is several years old, is that it is possible to generate minibrots of fractional orders with none of the discontinuities that spoil scenes and minibrots created the easy Z^(2.5)+C way.

The day here at Fractal Central began clear and frosty. It was reported that this morning's low of 34 was the coldest it has ever been in Central Pennsylvania this late in May. But once the sun got to work later in the morning, the temperature reached a rather pleasant 68F 20C. And yes, we do have kittens under the fractal back porch. Their mother had them out exploring the fractal yard this afternoon.

Well, I guess that's it for now. I'm sorry to hear that I should take it easy on the divisive philosophy for fear of causing too much off-topic debate. But as I see it, according to the scientists who have spent their lives studying such things, the sub-atomic world and fractals are actually the same things -- the mental images created in people's minds by the underlying numbers, and it's hard to accept a real objective world or a real fractal world made of building blocks that are no more solid than mathematical abstractions. If I'm wrong here, squelch the debate in the bud by showing where my thinking has gone astray.

If I see things getting too contentious on the list, I might start my own mailing list, where fractal philosophy will come first. I hope not, since I'm working on a few very interesting new Fractint formulas.

The next FOTX will be posted in a couple days. Until then, take care, and why does merely discussing reality cause such intense feelings? Maybe it's not fractally correct.

Jim Muth jimmuth@earthlink.net

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FOTX -- May 14, 2016 (Rating A-9,M-7)

Fractal visionaries and enthusiasts:

As today's unusually fast image shows, I am getting back into my old routine of finding rather attractive fractal patterns. I might not yet be in overdrive, but I am running in second gear at least. And do not expect one of those apocalyptic zooms to a ridiculous magnitude of something like 10^10000. Such zooms might make one gasp and say 'WOW' but at the end they all tend to look pretty much the same, admit it or not.

Today's FOTX, (The 'X' means I have not yet decided how often the FOT... will appear.), is a scene at a depth of a very modest 0.1 -- a Julia set of a point on the negative X-axis of the Z^4.01+C Mandeloid. In this case, the extra 0.01 in the exponent makes all the difference.

While pondering fractals over the past few months, I have also been pondering the old philosophical warhorse, the nature of reality. So far I have come to little in the way of an answer. In fact, I'm not even sure what the question is about. All I'm reasonably sure of is that I (whatever 'I' might be) am having a conscious experience. Whether the stuff around me commonly called material is real or not, it certainly does appear to be there. And if it is an illusion, does this mean nothing at all is there, or does it mean I am perceiving what is really there in a way that does not totally correspond to the true reality.

Be this as it may, the FOTX web site should be up and running again in a few days.

Today was partly cloudy with a temperature of 68F 20C and a few insignificant showers here at Fractal Central. The fractal cats spent most of their time doing what cats do best -- sleeping. Nicholas chose my favorite chair just after noon and lounged in it all afternoon. Between showers, FL did a little work in her garden, where the columbines are near their peak.

Until next time, take care, and if the theory of the Quantum had not been discovered, I might have run out of things to ponder after all this time.

Jim Muth jimmuth@earthlink.net

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FOTX0511 -- On_the_Half_Shell (Rating A-4,M-4)

Fractal visionaries and enthusiasts:

Today's minor effort is worth at least a quick look, though it will not set any records for beauty. It is a minibrot that lies on a tendril extending from a bud of the parent fractal that results when 1.6 parts of Z^-1.9 are combined with 0.2 parts of Z^-9.1. The shell-like effect that inspired the name was achieved by rendering the image with the outside set to 'tdis'

The good news is that my fingers really do remember the Fractint keystrokes, I just cannot think of the strokes when I consciously try to recall them, making frequent diversions to the help index necessary. I am also a bit rusty on finding minibrots and other good fractal scenes. A year ago, these fractal things were turning up almost automatically. Today, I needed to take time to try to guess where the scenic areas of the parent fractal might lie, if any might exist. My success was questionable.

Maybe I have become too involved in the debate over the meaning of quantum theory. The math of quantum theory is not in question, it works great. The problem is that the quantum world appears to consist of only the math that defines it. Things like electrons and photons can be seen as tiny balls, spread out waves, neither or both. In all cases the same math applies. The problem arises when the math is squeezed into our very limited, common sense idea of a world of 3-D space filled with real objects, which raises the measurement problem.

The measurement problem arises because the real world is made of sub-atomic particles, and the sub-atomic particles consist of numbers. The means that the real world is basically made of numbers, and numbers are pure abstractions, with no material reality at all. The problem is that no one can show with certainty how abstract numbers can create real physical material. Perhaps the greatest embarrassment of science is that even after 90 years of pondering, this problem is still unresolved.

Considering all this, it seems to me as if the real world might be much like a computer video game, where the fantasy world of the game exists only as program information until it is displayed on the screen, observed, and thereby made real. But if this is taken to be true, it will make no difference in everyday life, since everything we have always considered real will still appear and behave the same.

But rational materialists are quite upset by this. Maybe their concern is that their philosphical world view is being threatened. Quantum theory seems to be drifting toward mysticism, which is the antithesis of rational science and says that the material world is an illusion. In an effort to show how silly such views are, rationalists refer to such views, which are very common among new-agers, as 'Quantum Woo'. At the same time, Atheists are annoyed by quantum theory because it can easily be misused as an argument for the existence of God.

This debate is quite understandable. After all, everyone needs a solid foundation on which to base their life's philosophical standpoint, be it the white bearded old man in the sky of religion or the rock solid reality of the material universe on which science is based.

But fractals can be enjoyed by everyone, whether the images are real or not, or whether God exists or not, and the real world can likewise be enjoyed by everyone, even if it turns out to be no more real than fractals and if God is actually proved to exist.

There are problems with the FOTD web sites, so I'll not post any web addresses until the problems are resolved.

Today was cloudy and dreary but dry here at Fractal Central, with a temperature of 63F 17C. The fractal cats spent most of the day worrying about the feral tomcats that are again becoming more numerous around the area. And to make things worse, we think there could be kittens under the fractal back porch. FL is also rather down because the cool wet weather is causing her garden to lag. The next FOT... will be posted whenever it is. Until whenever, take care, and I'm either a believer or an Atheist, depending on how God is described.

Jim Muth jimmuth@earthlink.net

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