Art

Famous Fractal Artists

Today, you can find hundreds of digital artists all across the world who are making art that is incorporating fractal elements, and all these artists come with their own styles. Just take a look how many fractal art examples are on Pinterest or check out this video:

While algorithmic art is objectively showing the mathematical or geometric structure in a highly pleasing aesthetic way, there are also fractal artists who are daring to take it all to the next level and use fractal elements in their artworks that are appealing in a subjective way to spectators’ emotions and feelings.

In this article, I review the styles of Kerry Mitchell, Mark Townsend, and  Janet Parke, and you’ll notice that all three fractal artists come with their own recognizable and well-developed styles. …

Fractals of the Mist, Tangible Witchcraft, Meditation, and Prayer

We live in a country in which many are deeply religious, yet so few actually know about religion. This post addresses Fractals of the mist, Tangible Witchcraft, Meditation, and Prayer. According to a recent survey, not only do Americans know very little about people of other faiths and what they believe, but they also know precious little about their own religions!

That’s why I am glad for this new project, called Faithbook:
PBS (the Public Broadcast System, a TV station that is supported by donations (rather than advertising), for those readers outside the US) is hosting a new feature on their website, called Faithbook. Subtitled “God in America” it certainly is full of assumptions, but I will assume good intent.

The project is documenting how Americans actually feel about religion and spirituality in their own words, and you can browse what others believe, too. They ask a series of guided questions and people create their own profiles to answer them, so we get to see the diverse mosaic that is US culture. I have started my Faithbook page, and am answering the questions slowly.

I encourage all of you out there reading this to create a Faithbook page and answer the questions. If not for anyone else, certainly for yourself!

Learning UltraFractal

My love affair with web graphics started shortly after I did my first homepage back in June of 2012. It was a simple page, made up of graphics I found surfing the net. People on the web are incredibly generous in putting up great graphics and everything you need for a decent page can be grabbed with your browser or an FTP program.

The one limitation I ran up against very quickly was the size of the graphic. So I bought JASC Paintshop Pro from their website. It turned out to be a lucky choice. Not only could I re-size graphics, but I could add borders, text, contour, change their colors and more. Most of my 2012 Christmas graphics, my first venture into original stuff, were made with Paintshop.

At $65, Paintshop is a real bargain and will satisfy your urge for creativity for a long time. The tutorial that came on the CD ROM was excellent and there is more help now at the Paintshop site to get you started plus there are many websites that offer tutorials.
Which Is the Right Program for You?

No Artist Is An Island

It’s true.  We are all searching our “unique artistic voice” so that, as artists, we can make an impact on our community and one day, the world.  Many people want to “separate themselves from the pack” and be on their own path. But just because we want to be individuals in art – doesn’t mean we have to do it alone.

Look at all the great artists of our history.  Many of the famous creators from our past and present hung out with each other, learned from each other and collaborated with each other.

They understood that creating great art means you have to surround yourself with inspiring people.  Not so you can copy their work, but to be able to learn from their experiences and be inspired toward their own perspective.  Don’t believe me?

Fractal Art

Fractal Art consists primarily of mathematically-inspired, computer generated, abstract images that, in a very powerful way, are reflecting the beauty and intensity of mathematics, a facet that’s often overshadowed by the subject’s dry analyses and formulas.

Fractal Art images are generated by using fractals, and fractals are generated by repeatedly iterating a simple formula that uses complex numbers, meaning numbers that include 2 parts that correspond to a computer screen’s two dimensions.

These fractal images can be identified by their own characteristic pattern which is repeated at different scales all through the image. Fractals also come with the property that, in a mathematical sense, they are having infinite detail, meaning that you could zoom endlessly (sure, as far as your computer allows you to) into a fractal that will not change the structure.

These two features (the repeating pattern and infinite detail), make that fractals are used to picture to model various natural phenomena. There are people, and I am one, who find them very interesting. …

Fractal Art Exercise 3

There is no easy answer to your questions on iteration traps and patterns. It is important to separate the two issues in your own mind. They are completely different and independent concepts. Patterns originated as a routine called Cross Stitch that I never published.

The reason I didn’t publish it is that I knew that it would have to be used in conjunction with some sort of masking routine in order to be effective and I realized that it would be better to combine them. Since I had already written Iteration Traps, it made sense to combine them; hence, Iteration Trap Patterns.

The next video is also a helpful introduction to fractals:

Fractal Art Exercise 2

Select the eyedropper and click on the image somewhere near the center. The screen should go mostly, if not all, to the solid color. Put a decimal point before the 1 in the width input box. Now it reads 0.1. If nothing happened, put a zero between the decimal point and the 1, making it 0.01. Keep doing this until you see a (Solid color) stripe. This stripe will be up and down in your fractal.

See also this video:

Now, put the same number in the height box and you’ll have a circle. If you select the rectangle shape, it will change to a square. If you put different values in the height and width, you will get an ellipse or a rectangle instead of a circle or square. If the Rotation Angle of the fractal is not zero, the shape will move in the directions that were originally up and down or sideways.

In other words, if you change the Im- value, the shape will move parallel to the stripe you saw earlier. Bigger numbers in the positive direction will cause movement in the direction that was originally up and bigger negative numbers will cause downward movement. In the Rebox, positive is right and negative is left.

Fractal Art Exercise 1

Try…

1. Moving to the left by setting translation to -0.5
2. Moving to the left by setting location to -0.5

In the first case you can see the image shift within the sphere which it does not do in the second case. It’s a little confusing to visualize what’s happening here and that makes it hard to describe. Anyway, here’s a try at it and the nest video may also help:

When you move the ball to the side using the Translation value, the image is changed as if you stay in one place while the ball moves straight sidewise. Therefore, your perspective changes and you see more of the inside aspect and less of the part toward the outside of the window. If you move it using the Center coordinates on the Location Tab, it’s as if you move along with the ball, leaving your perspective unchanged.

Ultra Fractals and Psychedelic Fractals – a Brief Introduction

“Complex numbers” are two dimensional, which means that they’re made up of two parts: a “real” part and an “imaginary” part. The real part on its own is just an ordinary number and behaves as you’d expect it to. The imaginary part is something else again. Imaginary numbers have their own rules and often don’t behave as you expect numbers to do. So read on to learn more about Ultra Fractals and Psychedelic Fractals – a Brief Introduction.

The “Imaginary Unit” is “i”, which is sort of like the “one” for imaginary numbers. When you multiply i by i you don’t get i, you get minus one…a real number. That’s actually the formal definition of i…it’s the square root of minus one, but it also shows how strangely they can behave.

You’ll often see it written that imaginary numbers are just as “real” as real numbers, but I prefer to believe that real numbers are just as imaginary as imaginary numbers. …

Fractal Art – What Is It?

The question is simple, but the answer is very complicated and very long. So let’s take a look at Fractal Art – What Is It? Giving you a technical answer, though it may be accurate, won’t do much good as there will be so much typical ‘fractal-speak’, the jargon that not so many people understand. In high school, we learned that fractal is a never-ending pattern, and fractals are built by repeating something over and over again.

Last time I checked, how fractals are made was not a part of any high school curriculum yet lots of students want to learn all about fractals in math.

So let’s start learning about fractals, it’s so fascinating stuff!

A simple answer could be that fractals are shapes that, regardless whether you look at a fractal’s bigger or smaller part, have the same or similar, though not necessarily identical, appearance as its full shape. Take a rocky mountain for example.

You can see just how rocky it is from a distance, and up close, the rock’s surface is pretty similar. Little rocks come with similar bumpy surfaces as big rocks, just like the overall mountain.

The whole concept, or idea, of ‘self-similarity’ may be a little challenging to understand, yet it is an essential and fundamental element when it comes to understanding what fractals are. Smaller areas of a fractal shape are looking much like larger images. You can enlarge or zoom in as often as you want, but you will always see the same shapes and details, no matter how tiny the image of the full-size image.

This is what self-similarity is. Now when something is continuously so self-similar, what’s the point of zooming in, because, after all, everything looks the same. Small details look exactly like large details, so what’s the idea?

Not everything is so similar …
For fractal enthusiasts, fortunately, there’s more. A lot of types of fractals will appear wildly different when you’re zooming in. They still are self-similar, but not rigidly self-similar, and exactly this is what turns fractal exploration into something so intriguing. You will see something different every time you zoom in.

You may be surprised that, while there is so much familiarity, you’ll encounter unexpected new twists. Just one single fractal shape can always offer you something new to explore, and the further you’re zooming in, the more chances you’ll have to see something nobody has ever witnessed before. And today’s computers allow you easily to zoom, and zoom, and zoom …

How it works …
It’s not that difficult. Basic fractal techniques can be explained without needing to turn to confusing mathematical jargon and equations. You can start by giving every point on a screen a unique number. Take one number and put it into a specific formula. Then, put the outcome (the result) from the formula and put it back into that formula. Repeat this over and again, and see what will happen to the numbers that you get. Give each point a color based on what’s been happening.

That’s all. Really, that’s all there is to it. The thing is that with most formulas, this won’t result in anything interesting, but fractal creation is using formulas that allow very interesting things to happen. At times, the numbers resulting from feeding back the results into the formula, a process called iterating, will be exploding into huge numbers, that will just get bigger and bigger. These points will be colored in one way. At some other times, the numbers will get closer and closer to the original number, or ‘home in’. These will get colored differently.

The interesting thing here, and the reason why fractals are working at all is that there are times that the tiniest change in the number that you begin with, may result in totally different outcomes as you keep on iterating that number. And you’ll also see that the boundary between numbers that ‘home in’ and numbers that will explode is very complicated and twisted: this is the shape of a fractal.

An enormous task …
If you want to calculate fractals in this way, you’re faced an enormous task. A tiny fractal image, maybe just 640 x 480, is already containing more than 300,000 points, and each of these points may be needed to be run through your fractal formula over a thousand times. This implicates that the formula must be computed over three hundred million (!) times, and note that this is just a very mild example.

Bigger images, for example, poster-size fractals) may involve over a trillion calculations. Fortunately, modern-day computers are fast and can do that job in just a few minutes, though larger fractals may take hours or days to complete, the fact of the matter is that exploring fractals never was easier than today. Check also Las Vegas GED classes

And now …


As I said before, fractals are the main topic. So far, we’ve only been talking here about one specific type of fractals, the escape-time fractals, but we can find so many other types of fractals. Fact is, though, that if you dig deeper into fractals, you’ll need a lot more math to understand it. There are not so many books and publications related to fractals, and most web pages also don’t get so deep into heavy mathematics, so there’s a lot of work to be done, and a world of fascinations to explore.