## Fractal Art: An Introduction to Apophysis

With this tutorial you will find an introduction to the flame fractal program, Apophysis, and along the way you will learn how to create your first fractal. Apophysis can make a plethora of wonderful images, and your imagination is truly the only limit.
Before we actually make a fractal, it would be good to understand what we are getting into.
Dictionary.com defines a fractal as: A geometric pattern that is repeated (iterated) at ever smaller (or larger) scales to produce (self similar) irregular shapes and surfaces that cannot be represented by classical (Euclidian) geometry. Fractals are used especially in computer modeling of irregular patterns and structures found in nature.

Scientists and mathematicians have discovered how to use fractals to numerically describe coastlines, the shape of trees, our vascular system and much more.
Notice some everyday examples of fractals: the nautilus shell, romanesco broccoli, snowflakes, and the pineapple. As you look at each of these images, take note of the self-similarity and patterns.

In simple terms, fractal art is the graphical representation of a mathematical equation. Fractal art is infinitely diverse in form, color, lighting, and level of detail. Due to their mathematical foundation, fractals can have infinite detail: you can zoom in and out without limit (in theory). According to the definition above, fractals are also self-similar, but not identical, with regions of the fractal looking similar to other regions.

Many different types of fractal art can be created by means of different formulas. This series of tutorials will focus on the Apophysis program,  which uses iterated function systems or IFS. You can learn more about IFS in this Wikipedia article.

This can be a tricky subject, due to the many variations of the program currently available. Some of them work quite well, but are antiquated or do not support certain commonly used formulas (known as variations). To simplify matters, please use the Apophysis 7x16 version found at SourceForge.
Lets get started by opening Apophysis. On the first load you will be greeted with a randomly generated fractal. The interface may appear daunting at first, but we will explore the different options and settings progressively. The goal is to make the fractal you see at the beginning of this article.
Let’s begin by choosing a basic color palette so that the fractal will be visible while we work on it. Open the Gradient Selector (third button to the right of the quality text box, red square around it in the image below), and we'll begin by choosing a color palette. I generally will select a basic palette to work with and then adjust or completely change it as I work on a fractal. If you would like to reproduce the above fractal exactly, select gradient 498_beautiful.

Open the Editor. This is the small fx button in the toolbar as shown in the image below. The editor is where all of the heavy lifting is done inside Apophysis. You will notice an array of tools across the toolbar at the top of the editor. To get your feet wet we will be using a few of these in this tutorial.

Clear the randomly-generated flame to start with a blank canvas. Click the first button on the left of the toolbar to clear the editor and start with a new fractal flame. This creates a single transform, as indicated by the red triangle, with the linear variation (formula) applied to it. We'll look at variations in greater detail in upcoming tutorials.

Navigation is easy inside the editor. Right-clicking and dragging allows you to move around the editor. Use your mouse scroll button or the plus and minus keys to zoom in and out. Learn these simple navigation tools now and they will serve you well in your fractal adventures!
Now the stage has been set to design our first fractal. We have chosen a base color scheme, cleared the editor, and have a single transform ready to be modified.
Our first step is to change the size of the red triangle known inside Apophysis as Transform 1. On the right side of the editor there are several tabs and tools that allow us to apply changes to the transform. At the top you can always see which transform you are working with and switch easily to others by using the dropdown box.
The default tab is called Triangle. This tab allows us to modify the shape and positioning of the triangle. Click the smaller triangle on the left side of the 125 to make Transform 1 125% smaller. Now change this box to say 110 and click the small triangle again. We've shrunk the transform twice.

The next step is to duplicate the transform. This will transfer all properties of our current transform to a brand new one. Click the Duplicate Transform button at the top of the toolbar in the editor, the third button from the left. You will now see a yellow triangle representing Transform 2. These two transforms will make up the fractal.

Using the dropdown box on the right side of the editor, select Transform 1. Still inside the Triangle tab, locate the triangle movement controls that consist of four arrows and a 0.1 in the middle. The number in the middle indicates how many units to move the triangle, and these correspond with the grid in the editor. Change the 0.1 to 1 and click the Move to the Left arrow once. This moves Transform 1 one unit to the left.

Next we need to rotate Transform 1 90 degrees. The most efficient way to accomplish this is to click the left pointing arrow in the Rotation Controls (located just above the move controls in the previous step). This will rotate our triangle 90 degrees counter-clockwise. You'll also notice at this point that you now have something to look at in the preview window.

Now that we have the basics of moving and rotating, let's apply these to Transform 2. Select Transform 2 from the dropdown menu. Move it to the right by 1 unit. Rotate the transform by 90 degrees clockwise. You will now see a large rectangle in the preview window.

The next step is to introduce some color into the fractal. This process is highly dependent upon the gradient that we selected at the outset of the tutorial. Inside the editor, switch to the Colors tab. Click on the slider underneath the orange color and drag it around. As you drag this slider, notice in the preview window the effect it has on the coloring of the fractal. When you are finished exploring, drag the slider to the far right side, or simply enter 1.0 in the Transform Color box.

Up to this point, Apophysis is giving the same amount of priority to each transform. This is indicated by the 0.5 in the Weight box below each transform in the editor. When you create a blank flame, the default weight of a transform is 0.5. This is true for any new transforms you create as well. When you duplicate a transform, its weight is also duplicated. To clear up any misconception, if you set all transforms to a weight of 1, it would be the exact same thing as all of the transforms having a weight of 0.5. Either way they are all equal to each other.
Now we will direct Apophysis to give more priority to Transform 2 by changing the Weight to 1. Notice the change in appearance in the preview window. The details are now clearer.

At this point the colors on your fractal might appear slightly dull. This can be easily remedied. Close the editor window, as we will not need this any further. Click the Adjustment button, which is located between the Editor (fx) and Gradient buttons we used previously.
Inside this window, navigate to the Rendering tab with the purple gear. First change the Brightness setting (defaults to 4) to a 10. Sometimes modifying this one setting can make a drastic change in the appearance of your fractal. Be careful, however, because increasing this setting too much will lead to blowing out the levels and causing hot spots in your fractal, which can hurt people’s eyes!
While we are inside this window, change the Gamma setting to some different numbers. The best way to learn what this setting does is to experiment. You might liken it to the depth/amount of pixels that appear on the fractal; the higher the setting, the greater the pixels. Each fractal will benefit from you exploring this setting. When you are finished exploring, set the Gamma to 3.5.

The next step is to remove the obnoxious large black box that is currently around the outside of the fractal. We will use both the Move and Zoom tools in the main window to accomplish this. These tools are found on the right side of the toolbar in the main fractal window and look like a mouse (move tool) and magnifying glasses with a plus and minus for zooming in and out.
First, select the Zoom Tool (magnifying glass with the plus sign) to zoom in. Left-click and drag from the upper left-hand corner of the fractal down to the bottom right-hand corner. You might not be able to capture the entire fractal within the four corners of the window, so do your best to get as much of the fractal as possible and select what you think looks nicest.
Finally, select the Move Tool (mouse pointer) and use it to re-position the fractal so that none of the black sides are showing in the window. To do this, simply click and drag in the window. It may take a few tries to get the hang of it, and you may also need to switch back to the Zoom Tools. You should end up with something similar to the image below.

The last step is to render the fractal. Rendering is the process of having the computer run the formulas you have set up and output a high-quality final image. Click the Render button, which looks like a small purple gear in the main window toolbar, right after the open and save buttons.
In this window you can choose where to save the fractal and name it by clicking the Folder button on the top right-hand side of the window. You may want to change the file format from a png to a jpg unless you plan on editing the fractal in another image editing program.
The quality settings will greatly affect the final appearance of your fractal. Choose a Density setting of 10,000. Set the Filter Radius to 0.8 and Oversample to 2. Click Start to begin the rendering process. After several minutes your fractal will have rendered completely and be finished. Congratulations! You've created your first fractal.

Now, feel free to experiment more with the settings inside Apophysis. There are so many things you can create with just those few transforms. You can see a few examples of my own below.

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