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J Sonnentag

"Fibonacci Numbers and Nature"

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J Sonnentag

From the description:

Fibonacci numbers and the Golden Ratio have been found in art to be a classical pleasing set of numbers and ratio. But the numbers themselves are found all over nature, in striking ways, where they are not required for survival. The implications for design are discussed.

1. Kuhlemeier, C. 2017. Phyllotaxis. Current Biology 27: R882–R887. At http://www.cell.com/current-biology/fulltext/S0960-9822(17)30635-8
2. https://www.quora.com/Where-does-the-Fibonacci-series-exist-in-nature
3. https://www.quora.com/What-mathematical-properties-does-an-artichoke-have
4. https://evolutionnews.org/2017/09/plant-spiral-designs-still-unexplained/

 

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Gregory Matthews

Aubrey:  I have always been interested in Fractal Art as nature contains a lot of fractal images.

There is a branch of mathematics that deals with fractal geometry.  Some of their knowledge differs from that of the art world.

Briefly:  Fractal art/geometry consists of what might be a very detailed pattern that repeats itself on both smaller and larger scales.  I am looking for some detailed examples of this to post here in this tread.

For those of you who  may be interested  in this there is a website that will allow your do download, free of charge a mathematical program that will allow you to generate fractal figures.  As I just discovered this website a few minutes ago, I have not had time to check it out.  But, back I pre-historic times, long before Windows, I had a computer program that would allow me todo such and I had fun with it.

Well, to go back to searching for some examples of what I am talking about.

 

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Gregory Matthews

The following is an example of fractal art.  A detailed pattern is repeated over and over again in greater and lessor scale and the larger representations contain smaller versions within them.

There are mathematical equations that you can run on a computer that will generate them based on the numbers that you enter into the equation.

 

image.png

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Gregory Matthews

If you want to go deeply into the math, the following website will take you to the Quadratic Recurrence Equation that is behind the math:

http://mathworld.wolfram.com/MandelbrotSet.html

This was developed by Benoit Mandelbrot and the equations are often called the Mandelbrot Set.

I am looking for a website that will allow you to download a free program to generate such figure and does not contained a lot of embedded junk.

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The Wanderer
1 hour ago, Gregory Matthews said:

The following is an example of fractal art.  A detailed pattern is repeated over and over again in greater and lessor scale and the larger representations contain smaller versions within them.

There are mathematical equations that you can run on a computer that will generate them based on the numbers that you enter into the equation.

 

image.png

I am not into the math so much, but I have recently added this kind of art to my list of things that I like doing.Currently,I used a free program,such as The Gimp and several other programs that I dont understand; but they are fun to explore. Ill have to dig up some of my creations to show you. :)

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Gregory Matthews

Back in the Stone Age days when I had a 286 computer, Windows had not been developed and I ran PC DOS I had a program (Actually I still have it, but it won't run on a modern computer.) on a 5.25 inch floppy disk that ran a program that allowed me to generate fractal art images based upon my input to the various elements of the equation.

In my thinking, those were the days:  Of course,  your computer could not do even as mere fraction of what one can do today.  One had the choice of two (2) operating systems, either PC DOS or MS DOS.  I chose PC DOS and to this day I  like it and I still have the seven (7)  3.5 inch disks that were required to install it along with the books that explained the DOS commands that were useable with the OS.  Any time I wanted to install a program, I could enter DOS commands into the system that changed how the program was installed and operated.

Well, Windows 3.0, came along and with its development came a graphical interface.  With that computers began to be able to perform calculations and a lightening speed that ws well beyond what anyone had imagined before.  With that complexity the DOS commands that continued to be worked into the OS, and exist today, Passed beyond the ability of most people to use.  The simple books that explained those commands and how to use them in the OS expanded to books of over 1,000 pages and training to understand and manipulate the Windows OS became the work of formalized educational programs and Microsoft educational programs.

Well, the good old days are gone.  The new reality is here.  Now we can use our computers in ways that were never imagined in the past, but no longer can the common person take charge of how they actually operate and the common person must depend on other computer programs to do that.  Case in point:  "To install many programs on your computer today, you must use an installation program.  Or,  if you want to play a CD/DVD, you must use a program that is either built into your Windows OS, or, as In Windows 10 use another stand-alone program.  

 

 

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Aubrey

Boy! That was back in the day, wasn't it!! My brother and I used to play a maze version of D&D on my Dad's computer. He encouraged us to use it as much as possible (he was an IT professor at Washinton University). I think I was the only one of all my friends who knew how to program using DOS. When I met my future husband, he *had* to be a computer science major! LOL (Yep, I do think that math and art are in my blood.)

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Gregory Matthews

That 286 computer was a work  itself.  Using it I learned how to build my own computer and I eventually came to the place where I could walk into a store and walk out with a bag of parts that I cold put together into a working computer.   I have stopped building them as today I can purchase one for less than I could build the same one.   But, it has allowed me to purchase computers from Dell that were built to my specifications.  And, when my desktop arrived with a non-working system I was able to open it up, locate a simple wiring connection to the mother board and fix it.

By the way, for anyone who wants to build their own computers, I found the following to be very helpful:

Scott Mueller, Upgrading and Repairing PCs.  By Que. The last one I purchased had over 1,600 pages in it.  It is regularly upgraded to meet the current technology.

The current edition, I think, is the 22nd edition, which has some 1,100 + pages.  The last one that I used was the 11th edition.  

 

I found it to be very valuable to match the motherboard to the CPU and the other internal components.  Without such a source one who flies blind in building a computer may find that hey have purchased components the either do not do what they wanted them to do or can not be used in the selected motherboard (MB) and/or case.  Memory, hard drives must be matched to the MB   and some MBs will not fit in some cases.  The same is for video cards, if one choses to purchase one   instead of using the one integrated in the MB.

 

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The Wanderer
6 hours ago, Gregory Matthews said:

Back in the Stone Age days when I had a 286 computer, Windows had not been developed and I ran PC DOS I had a program (Actually I still have it, but it won't run on a modern computer.) on a 5.25 inch floppy disk that ran a program that allowed me to generate fractal art images based upon my input to the various elements of the equation.

I detest anything more modern than windows 7, but I imagine one day I will be forced to accept the new world order of computers. You brought back some very pleasant, Deja-vu here.I had a really heavy 286 compter back in the day as well, and it ran windows 3 point something.Then I got the first computer I remember well, as it was a "modern" 386, which looked really close to a freight train, and sounded like a helicopter taking off and ran windows 3.4 I think it was, along with Wordperfect 5. Talk about Dinosaurs, lol but it seemed to me that those old programs on the 5" disks were pretty cool. About two years ago, I got an old computer,and tried to connect to the internet with Windows 95. I actually did it,but it wasn't easy. I really liked that, and the 98 version as well.Still miss those. For basic word processing, one can easily make do with any version of windows, but its a lost cause, even for Windows XP a lot of times online now.Although I do know some hospitals in England and here were using XP until recently. Well, y story is getting too long here, but I do remember some really nice programs and I did use one of the early DOS programs for a form of fractal art. Its a lot of fun just for the creative end of it.

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The Wanderer
5 hours ago, Gregory Matthews said:

By the way, for anyone who wants to build their own computers, I found the following to be very helpful:

Scott Mueller, Upgrading and Repairing PCs.  By Que. The last one I purchased had over 1,600 pages in it.  It is regularly upgraded to meet the current technology.

The current edition, I think, is the 22nd edition, which has some 1,100 + pages.  The last one that I used was the 11th edition.  

I found it to be very valuable to match the motherboard to the CPU and the other internal components.  Without such a source one who flies blind in building a computer may find that hey have purchased components the either do not do what they wanted them to do or can not be used in the selected motherboard (MB) and/or case.  Memory, hard drives must be matched to the MB   and some MBs will not fit in some cases.  The same is for video cards, if one choses to purchase one   instead of using the one integrated in the MB.

I will check out that book.I have a little project I am thinking of doing. Hopefully, it is on Amazon? :)

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J Sonnentag
On 11/30/2017 at 3:35 AM, Gregory Matthews said:

Back in the Stone Age days when I had a 286 computer, Windows had not been developed and I ran PC DOS I had a program (Actually I still have it, but it won't run on a modern computer.) on a 5.25 inch floppy disk that ran a program that allowed me to generate fractal art images based upon my input to the various elements of the equation.

If you still have something to read 5.25" disks (I still have one thing here with such a drive) you could copy it off and try uploading to the internet archive.  They have an emulator that old things run on.  I just tested out Where in the World is Carmen San Diego Deluxe:D

https://archive.org/details/softwarelibrary_msdos

Running things in newer windows with the various compatibility settings on works for most things too.

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Gregory Matthews

Thanks.  I have the  disk someplace.  But, I probably do not have a drive capable of reading it.   However, I do have a 3.5" drive that     I can attach to my present computer through a USB port and read such.

I still have a fondness for PC DOS.

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Gregory Matthews

Fractal Art:

Software Programs:  The Wanderer has mentioned that he has used Gimp to generate fractal art.  I am told that program has a reasonable robust ability to generate fractal art.  I have searched  for a source for computer programs that can generate fractal art.  At this point in time, the best that I can come up with is:   http://fractalfoundation.org/resources/fractal-software/    I know that some  of their programs are free, but some may not be free.  I have not tried any of them out, so can not personally recommend any specific program.

NOTE:  I am not happy with any programs that I have downloaded and I am concerned about the safety of some.  However, I have not downloaded all.  So,, if you download and use, do so at your own risk.

Books on Fractal art:  I have both of the following in my library.  They are old, but I consider them to be of value  in learning about fractal art.  Even though they are old, both are available today from Amazon for a reasonable  price.

Jaudd Robbins.  Fun With Fractals.   Sybex,  1993, 220 pages.   This book gives an extensive discussion of the math that generates fractal images and how the software works.  I does NOT have any color art.  It contains chapters on a number of fractal computer programs.  If you do not have those programs, the book may be of limited value to you.

John Briggs. Fractals: The Patterns of Chaos.  Simon & Schuster, 1992,  192 large pages.  This book contains lots of color fractal art and additional B x W   art.  It also contains a section on various books and computer programs available at the time it was written.

 

NOTE:  I have downloaded a couple of the programs and after I run them I will let you know how they went.

 

 

 

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