mikegreenwald Loc: Illinois

Right on, a very clear explanation. Try graphing the super-simple equation "N=N+1"

Rongnongno Loc: FL

*ahem*

At the beginning of the 20th Century, mathematicians Pierre Fatou and Gaston Julia discovered fractal patterns while looking at complex mathematical systems. Back then, these objects defied linear analysis; they were considered aberrations or scary mathematical monsters, with infinite depth and complexity. They weren’t very popular and were forgotten, until the late Belgium mathematician Benoit Mandelbrot discovered them again while working at IBM labs in Armonk, New York in 1980.

Rongnongno Loc: FL

Funny how UHH users are searching 12:00 @ 14:00... ("Chercher midi a quatorze heure")

Very few are interested in mathematics and formulas when confronted with patterns. We simply recognize the beauty/fascination of what is in front of us in nature or otherwise. Plants have no idea what a fractal is yet use it. Plants among many other things. Yes, climate, disease, whatever destroy the pattern. To say that fractals do not exist in nature is interesting as mathematicians themselves use these samples to illustrate what a fractal is to neophytes like us. THEN they go into math and most of us go away...

Photographers use the term 'fractal' in ways that do not make much sense for math heads.
- Fractal originally comes from latin (fractus - verb frangere) which meant 'to break/broken'.
- This what optical filters do. They break the light to create patterns.
- Post processing filters do the same this and still use 'fractal' another misnomer.
- Then there are filters who truly use fractals formulas to enhance the edges and only the edges of an image and discard the rest. This is what we see in the stylized dragon image.

The rest? Math and naming? Interesting trivia. I learned about it in the 1990 when it was the rage of computing, folks going nuts creating mesmerizing time waster screen savers. A little bit of curiosity led me to learn enough to relate it to math and somehow this made me recall it was older than B.M so I searched for it.

I would not be surprised if it was even older (17th century - something I read long ago) if not even older. After all the Greeks deduced the existence of the molecule w/o proof using only observation. If someone knows about this, I am curious.

In any case B.M. is NOT the 'father' of fractal. He just made the word 'fractal' popular*. Remember Edison and Tesla??? Same thing.

-----
* 'Coined' as one put it in an earlier post.

russelray Loc: La Mesa CA

Mandelbrot coined the term "fractal."

russelray Loc: La Mesa CA

I know several thousand mathematicians throughout the world by means of my 47-year membership in The Fibonacci Association. I have never seen any of them use anything in nature as an example of fractals. simply because pure fractals do not exist in nature. The closest nature comes probably is the Romanesco broccoli and Orostachys 'Crazy Eddie." There are many things in nature that have some properties of fractals but those properties are more closely related to the golden segment, golden ratio, golden triangles, and golden spirals than pure fractals.

df61743 Loc: Corpus Christi, TX

Anecdotally, I worked for IBM in the 80's and focused on engineering and computer graphics applications such as CADAM, Catia, Caeds solids modelling. I became acquainted with and fascinated by the famous Mandelbrot turtle, and decided to write a program on a 80286 PC-AT in Basic to generate it. At that time, I believe the highest screen resolution possible was 640X480, and only fours colors were available. It took that PC about 11 hours to complete that recursive formula 307200 times to paint each pixel of that screen with one of those four colors.

Now, PCs can calculate the Mandelbrot set nearly immediately and display it in 64 million colors, much faster that the largest mainframe computers could in the 80s.

Dick

Rongnongno Loc: FL

Yet his name is cited more than than the other two...
The oldest reference is about 'recursion' made in 17th century. (funny that I remembered that useless trivia)
From there as all research becomes more refined it goes back to the Greeks and Persian mathematicians... I give up, I am not all that interested.


For those who are, universities such as Cornell offer online information that is... (*brain implosion*)

Rongnongno Loc: FL

I do not want you as a teacher.

Instead of going into vulgarization to explain something for the common person you insist on your exact math and are unable to related what fractals can be illustrated with.

This is likely why I despise math. You do not even see the applications around you or even the teaching aids you have around you.

Aerial antennas, yes, antennas, are just one fractal application but then again, when was the last time you looked up and saw how fractals are used without being aware of it? Yet their shape should give you a clue.

I just watched a youtube video made by two young female MIT students. The way they explain fractals in a simple, informative manner even it is only one type of fractal. NO MATH!!!! They pass the notion of repetition (recursion), scale, infinity and space to anyone who watches, listen and of course, is interested.

Rongnongno Loc: FL

hassighedgehog Loc: Corona, CA

Back years ago I had a Commodore 64 (or 128). On a floppy disc I had a program that had a fractal generator. I believe it was an early version of Printmaster. This is a greeting card, graphics program that was similar to Print Shop, but I considered it better. I did not use this very often as it took a loooooong time to generate anything. (only 64 or 128 KB--not even MB let alone GB). Printmaster still exists but as a much more sophisticated publishing program. I had both PrintMaster and Print Shop, so this may have been in the Print Shop program. It was in the early 80's.

BartHx

The methods and precision level for generating fractals can be various, though we cannot illustrate something that goes on to an infinite level. However, I have a way I used to use to illustrate the concept to my physics students. If you put a small drop of nail polish between two crossed microscope slides and then pull the slides apart, it will produce a fractal-like pattern. Once the polish has dried, there will be a repeating pattern that decreases in size and can easily be examined. With careful preparation, the smaller repeating patterns can even be viewed under a microscope.

lev29 Loc: Born and living in MA.

Russel, your reference of the above oeuvre prompted me to see if you had listed your website in the Links & Resources section, but I couldn’t find it. So then I tried using the Search function with the keyword Etsy and found a few results. Among them was an interesting topic posted on 10/03/2014, titled Is Etsy the New Silk Road for Copyright Infringement?, https://www.uglyhedgehog.com/t-249414-1.html.

NO ONE RESPONDED to the OP's post, which cited a Petapixel article with the identical title, found at https://petapixel.com/2014/10/03/etsy-new-silk-road-copyright-infringement/. Within this article is a presentation of the dialogue between the presumptive victim and a customer service rep at Etsy.

Then mentioned is a related article an attorney at this online journal: https://alj.artrepreneur.com/
I’m not sure which article it is, though both of the following have the word "Etsy" in their respective titles.
https://alj.artrepreneur.com/etsy-copyright-infringement/
https://alj.artrepreneur.com/etsy-store-stole-art-can/

Of course, I assume that you, Russel, were unaware of that October 2014 post on this forum.

Anyway, I subsequently looked up your website, https://www.etsy.com/, and in turn the item itself:
https://russelrayphotos2.com/2019/11/05/natures-geometry-succulents-now-for-sale/.
Interesting!

lev29 Loc: Born and living in MA.

Russel,

It appears that I made an error in assuming that www.Etsy.com is YOUR website! A non-photography friend of mine today informed me that Etsy.com acts as a marketplace for numerous vendors, such as yourself. Thus in retrospect, there is no specific reason for me to assume you were/are in charge of all of it.

So, please, if anyone has further thoughts concerning the topic of Fractals, please feel free to further elaborate.