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?

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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?

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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.

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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 next video is also a helpful introduction to fractals:

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.

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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.

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Fractal Art Exercise 1


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 next 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.

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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.

Because complex numbers are two-dimensional you can think of them as the points in a coordinate system. Usually the “Real Axis” is the horizontal axis and the “Imaginary Axis” is the vertical. This is the “Complex Number Plane”.

The axes cross at the “origin”, where both the real and imaginary parts of the complex number are zero. Your fractal window represents part of the complex number plane, and when there are no transformations active each pixel has a unique complex number.

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Fractal Art – What Is It?

The question Fractal Art, What Is It, is simple, but the answer is very complicated and very long. So let’s take a look at Fractal Art and what it is.

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.

The 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 of 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.

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