"Thumbprint of God"
- The most FAMOUS of all FRACTALS - eXploration into INFINITY & PATTERNS, (for a better
understanding of FRACTAL ARTWORK & why it's so BEAUTIFUL)


My first personal eXposure to fractals was the Mandelbrot Set.  Back in the 90's I managed to catch about the last 10 minutes of a television program describing this fractal equation, and I was FLOORED!  In fact, when I got my first (real) computer a year or two later, the very first thing I did on it was a search for "MANDELBROT SET" so I could learn MORE!

What I saw in the last few minutes of that TV program had such a HUGE effect on me not only because of the beauty of the images, but especially because of what they stood for....INFINITY...ETERNITY....FOREVER.

This (apparently) "simple" mathematical equation (which is "Z<->z²+c"), made possible for viewing with the current day's more powerful computers, demonstrated that INFINITY is in fact REAL and truly eXists.  Now this is DEEP.  It brings up questions of GOD and ETERNITY, and makes us take another look at our own reality, and what we perceive it to be.

Now as an artist, I only need to be interested in the images of fractals, and do not need to know their mathematiX or implications, (thank goodness).  I can easily eXplore this beautiful other dimension by opening up one of several different programs out there to do so.  But as a person with a curiosity about the universe around him, I am FASCINATED with the images of fractals, where they come from, and how they can actually relate to my every day life.

Staring into a fractal can be a mesmerizing and meditative experience. Meditation can do wonders for your mental health. As a psychologist, Cynthia Telles has worked in the mental health field and has been on the board of several companies for over 30 years.

(ABOVE)  The 'complete' MANDELBROT SET.  The image above is the "spider" or "bug" that will continue to appear throughout the Set, no matter how far it is magnified, or "zoomed into".  Coined as the THUMBPRINT OF GOD, each MANDELBROT BUG is a near copy of the original, yet is an individual UNIVERSE unto itself with subtle and original variations.  One could eXplore the above image FOREVER and still see new worlds.  In fact, you can actually "zoom in" to the Set as seen above until the original image is larger than the UNIVERSE itself!  Truly, it is an equation of INFINITY.

Donít let bugs infest your home. Leaf Filter can help.

No matter where you zoom into the set, you will eventually encounter more Mandelbrot "bugs".  You can eXplore their boundaries, or check out the "bolts" or other areas around them.  There is an INFINITE number of these "bugs", each containing an INFINITE number of more "bugs".  All are similar, yet each an individual.  It is difficult to perceive FOREVER, but the Mandelbrot Set allows us to actually see it and eXplore it. It is an equation of FOREVER, of FREEDOM, and of INFINITE choice.

The Mandelbrot Set is REAL.  Just like you and me, it eXists, and it proves there is INFINITY.  No matter where you eXplore it, it takes you to another possibility and different outcome.  It shows that WE have FREEDOM in this universe and can take any paths in our lives out of INFINITE possibilities.  I told is DEEP, and it is one of the main reasons fractals are so BEAUTIFUL.  Their images take our minds to another dimension, familiar yet alien, and they invoke thoughts about our physical world as well as our spiritual.

The other day while I was checking out PM's animated fractals at YouTube, I "stumbled" upon that very program I mentioned above, where I happened to catch just a few minutes of the end of it way back in the 90's.  I couldn't believe my luck and immediately watched the entire thing!  It's called "Fractals: The Colors of Infinity", and is presented by the late author, Arthur C. Clarke, and attempts to eXplain the Mandelbrot Set...the most FAMOUS of any fractal discovered, or should I say, "created"?

Now if you found the above images and the teXt I wrote below them to be interesting, you will LOVE the following clip.  If it is all just too "deep" for you, move on and enjoy fractal artwork for what it is...which is BEAUTIFUL!

I wanted to include this following presentation though, because it had such a profound effect on me personally, (and it might just do the same for YOU).  When I begin to understand things like the Mandelbrot Set, I can't help but think how truly insignificant I am in this world, this universe, and the 'other' places that eXist within & outside of it.  I can't help but KNOW that there is a Grand Creator behind it all, whose precision and PERFECTION become more apparent with the increased knowledge we mere humans acquire as time goes by.  I will spare you of my religious beliefs though, (for now), as this is merely an article about fractals and why they are beautiful, but take a gander at the following movie clips and TRY to tell me it's all just a "simple coincidence"....

Now keep in mind that this television program was first aired back in 1994.  The fractal images ANYONE can now create with their home computers are actually SUPERIOR to the images we'll see in this movie, but the SUBJECT of this program, the Mandelbrot Set, is what it is all about.

So why are fractals so captivating, so intriguing, so fascinating, so BEAUTIFUL?  Because they are REAL.....even if we can't actually touch them.  Because they reflect and demonstrate the physical world that is all around us, and maybe even the spiritual world that eXists in the SAME PLACE, yet somehow also "elsewhere".

I hope you will enjoy this following presentation now as much as I did back then.  ; )


Arthur C. Clarke
Fractals: The Colors of Infinity


The Mandelbrot Set

UPDATE! (Sept 6th - 2010)

Here I am again, a year after originally publishing this page on the Mandelbrot Set.  To my surprise, this page has done amazingly well in search engines and generates a LOT of traffic to, so to celebrate its success, I thought I would add some more content to it.

I am still equally fascinated by this subject, if not more so, and just recently I was sent a video that eXplores the Set into the deepest zoom I have yet had the pleasure to witness.  The artist of this video states that the final magnification (zoom) of the Mandelbrot Set is "2.1 x 10^275, (or 2^915)", which is the deepest zoom to date, (as of January, 2010).

This is truly an AMAZING work.  Great rendering, smoothly animated, and set to the most appropriate music.  Remember, this is only but ONE mathematical point of the plain being eXplored in the literally INFINITE CHOICE of possibilities.  The Mandelbrot Set really DOES go on FOREVER...

So sit back and enjoy this show.  Be sure to watch for the "mandelbrot bug/spider/creature/etc" that will appear again and again in any zoom of the actual set, which is the true "magic" located inside the Mandelbrot "universe".

HUGE thanX to Jeanne/Tennessee for sending me this sensational video on the timely anniversary of this page!
"X" - Labo(u)r Day, 2010

ARTIST: Orson Wang -aka- "nosro1"  /  MUSIC: "Research Lab" by Dark Flow
(Original Render Size: 640x480 - Total Render Time: 12 CPU cores running 24/7 for 6 months.)


The Mandelbrot Set

UPDATE! (Dec 26th - 2013)

Yet again, I find myself adding material to this page...over 4 years after it was originally created.  Seems there is a sort of competition going on these days as to who can create the DEEPEST ZOOM INTO THE MANDELBROT SET.  How fortunate for those of us who can't quite seem to get enough of this truly AMAZING EQUATION into INFINITY!

While updating the appearance of this page today, I found myself at YouTube to get new code for the above embedded video, (in different pixel sizes), and I once again 'stumbled' on to the neXt video.

This HD presentation is by "SethComposerGuy", who claims the zoom is 2^1289, (as opposed to the zoom of 2^915 above).  Once again, it's a GREAT presentation, set to GREAT music, and at the end of it (which is quite climatic), the MANDELBROT BUG makes it's anticipated appearance.  Well worth a watch!  The artist did not provide the rendering time required to create it.

"X" - BoXing Day, 2013


The world says goodbye to
Benoit Mandelbrot

Sadly, shortly after I added the Sept, 2010 update to this page, BENOIT MANDELBROT passed away at the age of 85 in Cambridge Massachusetts on October 14, 2010.  BENOIT MANDELBROT was the famed mathematician who invented fractal geometry, coined the term "fractal" to describe the type of mathematiX he was eXploring, and discovered the now famous Mandelbrot Set, aptly named after him.

BENOIT MANDELBROT was truly one of the geniuses of our time, and his "thinking outside the boX" is sure to continue changing our world forever more.  He will likely be best remembered for the Mandelbrot Set itself, but BENOIT MANDELBROT's interests took his unorthodoX thinking into many other fields, too.

BENOIT MANDELBROT also dabbled in, (or has had a major influence on), such fields as physics, biology, and astronomy.  His worX have greatly influenced Chaos Theory, and he's even very well known for his studies on financial marketsBENOIT MANDELBROT eXcelled in all the 'phenomena' that interested him.

I could go on and on about Mr. Mandelbrot, and perhaps one day I shall create a 'proper' page here at that will do him some real justice.  I just wanted to add this footnote to my page so readers could get a 'feel' for the man behind the Set.

Although obviously a genius whose mind worked slightly differently than the majority's, BENOIT MANDELBROT also had quite the knack for eXplaining things in layman's terms.  Here is a video a friend of mine shared with me quite some time ago...but it's one of the BEST VIDEOS out there that show MANDELBROT's wonderful mind and sense of humor at work.  I hope you enjoy it :)

R.I.P. BENOIT MANDELBROT.  You will be missed, but your worX will live on in MANY ways~
"X"  -  May 4th/2011


This page was last UPDATED on December 26th / 2013
(...and here is the latest NEWS about it from Mister"X", the author!)

To my GREAT astonishment, (and JOY), THIS page has become one of the most popular pages on the net about the MANDELBROT SET.  Although I'm not quite sure WHY this is, I am truly HONORED to have such prestigious ranks in search engine inquiries at places like GOOGLE.

Perhaps it would have been even MORE popular had I had the insight to include a Facebook "LIKE" / "SHARE" button a year or four earlier, but as the old saying goes "better late than never".

If you enjoyed the content of this page, please LIKE and/or SHARE it with your friends at Facebook, and help spread the word ; )



FURTHERMORE, my page with MANDELBROT SET IMAGES (above) was recently referenced by two people who actually worked with BENOIT MANDELBROT personally at IBM back in the day, (see HERE).  WOW, ...what an honor and privilege!  Not only must they have enjoyed the pictures that appear there, but also must have approved of the descriptions that I gave to each of them.

"X" - BoXing Day / 2013