FOTD -- September 14, 2014 (Rating A-8,M-7)

Fractal visionaries and enthusiasts:

Today's image shows some of what happens when the expression Z^(1.75)+C is iterated in Mandelbrot mode a mere one-half level up the complex logarithmic hyperspiral. The parent fractal is little more than a shapeless blob somewhat resembling a squashed bug. Today's scene is located on a filament extending from the small period-5 bud on the southest side of the main bay.

The art rates an 8, mostly because of the unusual color scheme, which came about almost totally by accident. The effect of small terraces was achieved by rendering the scene with the outside set to 'tdis'.

The math rates a 7. I rated it because I was rather impressed with the near perfection of the central minibrot, which is quite well shaped, especially considering the chaotic shape of the parent fractal. In fact, the minibrot could almost pass for an everyday distorted quadratic minibrot.

The surprisingly undistorted shape of this minibrot inspired the name "Small But Impressive".

The calculation time of 2-1/4 minutes is well within reason, and the web sites are there to make the task even easier.

So join the trendy set. Check the FOTD web sites at:

<http://www.crosscanpuzzles.com/Archives.html>

<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>

<http://www.Nahee.com/FOTD/>

<http://user.xmission.com/~legalize/fractals/fotd/about.html>

Today, the second Sunday in September, turned out pleasantly brisk here at Fractal Central, with a mix of sun and clouds, a bracing north wind and an afternoon high temperature of 64F 18C. At least the fractal cats must have thought so, since they checked the outside conditions from their window shelf almost constantly. The fractal humans meanwhile checked very little of anything.

The next FOTD will be posted in a day or two or three. Don't be surprised if it actually appears in one day. Until whenever, take care, and I can't wait to not buy the latest electronic gadget, though one of these days I might actually pick up one of those throw-away cell phones. As for now, how do I get along without a cell phone? . . . Actually quite well!

Jim Muth jimmuth@earthlink.net

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FOTD -- September 11, 2014 (Rating A-8,M-8)

Fractal visionaries and enthusiasts:

Today is the 13th anniversary of the 9-11 attack, so in honor of the grisly occasion I have found a fiery looking fractal. I named the image "Fiery Fingers" quite naturally.

The parent fractal is the Z^(1.00625)+C Mandeloid as it appears only one turn up the complex hyperspiral. This parent resembles the typical bullet that is so common in fractals in this range of exponents. In fact, the exponent of Z in today's image, 1.00625, is as close to unity as I have yet come.

In this ultra low range, very little chaos remains, but there is some, and the next FOTD will show a scene in this unlikely chaos. Today's scene shows no chaos, but rather a field of branch-cut discontinuities resembling a large fire.

The fiery effect is totally due to the coloring, which earns the image an artistic value of an 8. The math also earns an 8, due to the ridiculously low value of the exponent of Z, which produces a fractal anyway.

The calculation time is the big loser. The 9-1/3 minutes required to complete the image is far more than the scene is worth. But once again, the web sites rush to the rescue.

The official FOTD web site is now up and running. It may be accessed at:

<http://www.crosscanpuzzles.com/Archives.html>

The other sites are at:

<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>

<http://www.Nahee.com/FOTD/>

<http://user.xmission.com/~legalize/fractals/fotd/about.html>

The weather here at Fractal Central today was nondescript. The day brought some clouds, some sun, a few light sprinkles and a temperature of 81F 77C. It amounted to a day to soon be forgotten. The fractal cats forgot the day as soon as it began, with Lida and Jasmine chasing each other up and down the hallway most of the morning, while Nicholas watched the silly girls with curiosity.

The next FOTD, which will be very chaotic, will be posted in a day or two or three. Until the moment of revelation arrives, take care, and I want to be a version of me that exists in an alternate reality where total peace prevails.

Jim Muth jimmuth@earthlink.net

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FOTD -- September 08, 2014 (Rating A-7,M-8)

Fractal visionaries and enthusiasts:

Today's scene, which lies just beyond the range of perfect resolution, is named "Another First". The reason for the name is that the central minibrot is the first one I have stumbled upon that is so obviously divided into two separate parts.

The formula that created today's Mandeloid image is Z^(1.09)+C. I calculated this formula a mere 0.75 levels up the hyperspiral, which created a parent shaped like a bullet or torpedo diving to the southeast. This bullet shape is quite common in Mandeloids with an exponent of Z only a small amount greater than unity.

Today's scene lies in a large field of debris near the northwest limit of its parent. The image rates a 7 for its artistic value and an 8 for its math value. The calculation time of over 8 minutes is mercilessly slow, making a visit to the web sites the better choice.

Unfortunately, the official FOTD web site is temporarily down for repairs, but the finished image is or soon will be posted to the following three sites:

<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>

<http://www.Nahee.com/FOTD/>

<http://user.xmission.com/~legalize/fractals/fotd/about.html>

The temperature of 77F 25C here at Fractal Central today was near perfect, but too many clouds filled the sky to call the day absolutely perfect. The fractal cats agreed. Eleven-year-old all-black Nicholas watched curiously as one-year-old Jasmine and 4-month-old Lida chased each other up and down the fractal hallway until both ran out of steam and collapsed into exhausted heaps. The fractal humans, who must keep going even when the steam runs out, had a near normal but busy day.

The next FOTD will be posted whenever it is. (Yes, there will be more FOTD's. The current slowdown is due to renovations here at FC.) Until that cosmic moment of renewal arrives, take care, and keep abreast of the anachronistic FOTD. It's a real blast from the past!

Jim Muth jimmuth@earthlink.net

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FOTD -- September 04, 2014 (Rating A-7,M-8)

Fractal visionaries and enthusiasts:

If anyone is still checking the list, the fractals will continue coming, maybe not every day but often enough to make a quick check always worth the effort.

Today's image shows one of the more interesting minibrots I have yet found in a fractal with an exponent of Z between one and two. The exponent of Z in today's image is 1.77, and the complex logatithmic hyperspiral was sliced 2 turns from ground zero in the positive direction.

The parent fractal resembles a distorted Mandelbrot set rotated so that the large bud faces southeast, with the nascent East Valley on the northwest side of the main bay. Today's image with its central minibrot lies on the northeast shore line of this rudimentary valley.

I named the image "Island Universe" because the central minibrot, like all minibrots, contains an infinity of detail within its basin of attraction.

The art aspect rates a 7 since I could have done more work on the coloring. The math rates an 8 because of the unusual richness of the scene with its shoestrings around the minibrot.

The image calculates in 3 minutes -- about average for an everyday fractal. The image may also be enjoyed on the FOTD web sites.

The image is online at:

<http://www.crosscanpuzzles.com/Archives.html>

<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>

<http://www.Nahee.com/FOTD/>

<http://user.xmission.com/~legalize/fractals/fotd/about.html>

A mix of sun and clouds with a temperature of 86F 30C made today an enjoyable one here at Fractal Central. The trio of fractal cats agreed. The 11-year-old cat Nicholas slept while the one-year-old kitten Jasmine and the four-and-one-half-month-old kitten Lida Rose kept each other busy playing.

The next FOTD will be posted in a day or so. Until whenever, take care, and when one side says 'We will stop bombing you when you stop terrorizing us' and the other side says 'We will stop terrorizing you when you stop bombing us', nothing gets done.

Jim Muth jimmuth@earthlink.net

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FOTD -- August 31, 2014 (Rating A-6,M-5)

Fractal visionaries and enthusiasts:

Today's fractal image is simply one end of a parent fractal, which is shaped like a bullet. (One outzoom will reveal the entire bullet.) I named the image "A Strange Scene", since it certainly is rather strange, but then, all fractals are strange in some ways. I could rate the themeless artistic aspect of today's image no higher than a 6, and the math, which has been used countless times before, rates only a mediocre 5.

The calculation time is an unusually slow 13 minutes, which definitely will lead to boredom and perhaps the mortal sin of rendering the image at thumbnail size to see if it is worth the effort of calculating at full size. Luckily, the web sites are there to eliminate such difficult decisions.

So eliminate tough decisions View the finished image on the FOTD web sites at:

<http://www.crosscanpuzzles.com/Archives.html>

<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>

<http://www.Nahee.com/FOTD/>

<http://user.xmission.com/~legalize/fractals/fotd/about.html>

A cloudy day with occasional showers and a temperature of 79F 26C passed quietly here at Fractal Central today. The fractal humans spent the day peacefully, while the three fractal cats had a relatively peaceful day also.

The next FOTD will be posted -- this much is for sure -- but who knows exactly when that magic moment will arrive. Until whenever, take care, and it appears to me that our western scientific paradigm has assumed the rigidity of a religious dogma, with its structure being held in place by the power of polarized language such as real/imaginary, exists/does not exist, objective/subjective, true/untrue, and so on. Oh well, as long as we are protected from the threat of belief in irrational superstition, I guess it doesn't matter.

Jim Muth jimmuth@earthlink.net

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FOTD -- August 28, 2014 (Rating A-8,M-6)

Fractal visionaries and enthusiasts:

Today's new formula is the ultimate speed-up for the branch-cut series. It was suggested by Hal, which explains the 'H' at the end of the formula name. The 'J' refers to my humble self.

The name of the image, "Spiralling Inward", refers to the vaguely spiral arms radiating from the Z^(1.1892)+C minibrot at the center. The parent fractal is notably un-impressive, consisting of little more than a shapeless blob with a hernia. Today's scene is located in debris attached to the hernia, which actually is a large period-2 bud.

The art rates an 8 because of the extra effort I put into the coloring. The math rates a lower 6 because the image holds nothing new.

The calculation time of 1-1/2 minutes is fast enough to prevent impatience and slow enough for some anticipation to build. And as always, the web sites are always there for instant relief.

Be smart! Avoid calculation by checking the image already calculated on the FOTD web sites a;:

<http://www.crosscanpuzzles.com/Archives.html>

<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>

<http://www.Nahee.com/FOTD/>

<http://user.xmission.com/~legalize/fractals/fotd/about.html>

Absolutely perfect weather prevailed all day here at Fractal Central today. (Absolutely prefect weather is defined as a temperature of 77F 25C, deep blue sky decorated with cottonpuff clouds, low humidity and a refreshing breeze from the north.) The fractal cats and humans all enjoyed the conditions to the best of their abilities.

The next FOTD will be posted who knows when. To find out when, check back occasionally. Until whenever, take care, and Robin Hood's political leaning was definitely toward the progressive end of the spectrum. Prince John and the Sheriff of Nottingham were far more conservative.

Jim Muth jimmuth@earthlink.net

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FOTD -- August 25, 2014 (Rating A-5,M-6)

Fractal visionaries and enthusiasts:

Today's image might not be the best of all time, but it does show what happens to spirals in fractals of very low order. The parent fractal is the Z^(1.1)+C Mandeloid. At ground level this Mandeloid is little more than a tiny kidney bean, but when sliced at a level 0.5 turns up the hyperspiral, it opens up into a giant torpedo-shaped bay surrounded by scads of interesting details. Just north of the main torpedo lies a chaotic spiral, which is rather hard to pick out. Today's scene lies deep in this spiral.

I could give the art a rating no higher than a 5, while the math rates a 6.

The calculation time could be the best feature of today's FOTD. The 40-second wait is about as brief as calculation times come. Of course, the web sites are always online to make the viewing even simpler.

The finished image for all it's worth is posted online at:

<http://www.crosscanpuzzles.com/Archives.html>

<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>

<http://www.Nahee.com/FOTD/>

<http://user.xmission.com/~legalize/fractals/fotd/about.html>

Absolutely perfect weather prevailed here at Fractal Central today, with all parameters as near perfect as possible. The fractal cat trio is now pretty used to having the other two around, though an occasional curse word does still slip out. The humans, thankful that the newcomer fractal cat is being accepted into the family, had a busy but otherwise uneventful day.

The next FOTD will be posted within a reasonable time. Until reason prevails, take care, and there really are problems with no solutions.

Jim Muth jimmuth@earthlink.net

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FOTD -- August 24, 2014 (Rating A-8,M-7)

Fractal visionaries and enthusiasts:

With a new fractal cat on the loose here at Fractal Central, things have been busy, busy, busy. But they have not been too busy to dredge up another fractal, which is no surprise. After all, the supply of fractals is limitless.

I found today's mini-wonder along the main spike of the Z^(2.001)+C minibrot at the tiny level of 0.001 turns down the hyperspiral, where the large minibrot on the spike is just starting to split apart. The exact location is in the debris where the main bud of the minibrot has come apart.

The name "A Forgotten Region" refers to the fact that all fractals are only potentially real until they are stumbled upon by an intrepid explorer (like myself).

The art rates an 8 because this describes the effort I put into the coloring. The calculation time of 40 seconds is mercifully brief, making viewing the image a pleasure rather than a chore. And the web sites can make things even better.

Check the finished image at:

<http://www.crosscanpuzzles.com/Archives.html>

<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>

<http://www.Nahee.com/FOTD/>

<http://user.xmission.com/~legalize/fractals/fotd/about.html>

A perfect day passed here at Fractal Central today, with a temperature of 79F 26C and photoshop blue skies decorated with cottonpuff white clouds. The fractal cats enjoyed the conditions as much as possible, while the humans did the same.

The next FOTD will be posted in the near future. A picture of the new fractal cat will also be posted shortly. To find out how near the future will be, check back early and often. Until next time, take care, and pay no attention to the things those ignorant ________ on the other political side are saying.

Jim Muth jimmuth@earthlink.net

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FOTD -- August 22, 2014 (Rating A-8,M-7)

Fractal visionaries and enthusiasts:

In the Z^(2.003) Mandeloid there are curious rectangles near the X-axis just east of the large minibrot, which are especially prominent in the Julia sets of the area. Today I wondered what exists in this same area of the Z^(2.002) Mandeloid.

What I found is a kind of proto-rectangle, filled with a slew of intricate and quite decorative detail. As is the case with the Z^(2.003) rectangle, a tiny change in the 'C' value makes a great change in the image. Today's image shows one of the more impressive aspects of this protorectangle.

The reason for the name "Rectalgle's Cousin" is obvious. The calculation time of a zippy 35 seconds will pass in a flash and a half. And as always, calculation may be totally avoided by checking the web sites.

The finished image is posted at:

<http://www.crosscanpuzzles.com/Archives.html>

<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>

<http://www.Nahee.com/FOTD/>

<http://user.xmission.com/~legalize/fractals/fotd/about.html>

After a torrential thunder-storm yesterday, which flooded the basement of the local city hall, today was much calmer here at Fractal Central, with partly cloudy skies and a temperature of 81F 27C. The three fractal cats, (Nicholas and Jasmine have been joined by a four-month-old kitten probably named Lida.), spent most of the afternoon resting after spending the morning becoming more familiar with one another.

The next FOTD will be posted in due time. Until the time is due, take care, and why can't I shake the nagging impression that the U.S. government itself is responsible for much of the continuing unrest in the world, especially the Middle East?

Jim Muth jimmuth@earthlink.net

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FOTD -- August 19, 2014 (Rating A-8,M-5)

Fractal visionaries and enthusiasts:

The name of today's FOTD, "1.4142_Minibrot", says it all. The image is a view of a minibrot in the Z^(sqrt(2))+C Mandeloid as it appears at a level of 1.373 turns up the hyperspiral. At this not very lofty height the parent fractal resembles nothing as much as a lima bean with a short filament extending southwest and a long but disconnected filament extending north. Today's scene is located in the East Valley of a larger minibrot on the northern filament.

Actually the hyperspiral does not produce an infinite variety of fractals, but is a loop of 4.4428828..., at which point the fractal returns to the one that exists at the zero level and starts the cycle over.

The art rates an honest 8. I spent near a half hour on the colors. With a rating of 5, the math falls short however. The math is now old stuff.

The calculation time of 1-1/2 minutes is fast enough to avoid impatience, and slow enough to enjoy the unfolding of the scene. And as always, instant relief is available on the web sites.

Check the finished image at:

<http://www.crosscanpuzzles.com/Archives.html>

<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>

<http://www.Nahee.com/FOTD/>

<http://user.xmission.com/~legalize/fractals/fotd/about.html>

The weather was perfectly average here at FC today, with hazy sun and a temperature of 81F 27C. The fractal cats agreed. The humans also agreed. Until the next FOTD appears in a day or two or three, take care, and wonder what it's all about.

Jim Muth jimmuth@earthlink.net

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FOTD -- August 18, 2014 (Rating A-6,M-7)

Fractal visionaries and enthusiasts:

Today's image is named "Blattaria_Specimen", and the image certainly does resemble a specimen of the order. Actually, the image is a Julia set of the valley at the western extremity of the main bay of the Z^(1.05)+C Mandeloid as calculated at a tiny 0.024 turns up the complex logarithmic hyperspiral and a little into the imag(y) direction.

The art rates a 6; we have been here several times before. The math rates a 7; we have been here before but not at this level of the hyperspiral.

The calculation time of 1-1/2 minutes will pass in a semi-flash. The web sites will eliminate the flash.

The finished image is available online at:

<http://www.crosscanpuzzles.com/Archives.html>

<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>

<http://www.Nahee.com/FOTD/>

<http://user.xmission.com/~legalize/fractals/fotd/about.html>

Perfect weather prevailed here at Fractal Central today. Perfection is described as blue skies decorated with puffy white clouds, low humidity, and a temperature of 79F 26C. The fractal cats had a mostly pleasant day, but did get into a tussle when Jasmine leaped from the couch onto Nicholas and caused his tail to puff up. The humans spent the day working.

The next FOTD will be posted in a day or two or maybe three or four. Until whenever, take care and I have nothing to say about current events in Saint Louis except that I am disappointed that the same old problem still exists even 50 years after the Civil Rights Act was passed, and after 50 years of the best-intended efforts to eliminate discrimination and poverty, and finally achieve true equality. It is actually starting to appear, at least to me, that achieving equality might be a wishful myth.

Jim Muth jimmuth@earthlink.net

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FOTD -- August 14, 2014 (Rating A-6,M-7)

Fractal visionaries and enthusiasts:

Today's image is titled "Rectangle Break-Up" because that's exactly what it is. Like the previous image, it shows one of the strange rectangles in the Julia aspect of the Z^(2.003)+C Julibrot in a state of partial disintegration.

The art rates a 6, the math, a 7. The calculation time of one measly minute will cause no impatience. And as always, the web sites can eliminate calculation completely.

I'll continue exploring different aspects of the rectangle in the next few FOTD's. Then we'll move on to new and hopefully greater fractal things.

Check the image on the FOTD web sites at:

<http://www.crosscanpuzzles.com/Archives.html>

<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>

<http://www.Nahee.com/FOTD/>

<http://user.xmission.com/~legalize/fractals/fotd/about.html>

Near perfect weather prevailed here at Fractal Central today, with a mix of sun and clouds, low humidity, refreshing breezes and a temperature of 77F 25C. Both the cats and the humans enjoyed the fine day.

The next FOTD will be posted in a day or two. Until then, take care, and people will never learn to get along together until they are willing to hear and understand the views and problems of the other side.

Jim Muth jimmuth@earthlink.net

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