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Apophysis - Flame Fractals

Updated on January 8, 2015

Computer Generated Mathematical Art

I have artistic inclinations, but I can't draw worth a hoot. So I make fractals instead.

Fractal images are produced by plotting the graph of mathematical functions. There are various computer programs that people use to design the fractal image, and each program then tells the computer what color to make each pixel of the image. So what is a flame fractal? you might ask. I can't tell you what makes it different from other fractal images, but I can usually tell one when I see it. There is an explanation here, if you can make sense of it. I can't.

Fractal Flame

Fortunately, you don't have to know much about the mathematics to be a good fractal artist.

As I mentioned, I can't draw, but I can move a mean computer mouse!

In my earlier Lens on fractals, I presented fractals made in Ultrafractal and Xenodream. These are not flame fractals. But the Lens was too long for me to include the Apophysis images there, especially since I have lots more of them.

Apophysis is freeware and open source. Many people have contributed to its development. You can download the program here:


You can see my fractal gallery with prints for sale here:

Pat Goltz Gallery

Use "Apophysis" as a search term to get all the images made with Apophysis. Use "fractal" as a search term to get all my fractal images. There is a separate selection of my best images; scroll down and look for it on the left.

There is a thriving Apophysis community on deviantART, where I have most of my flame fractals for sale. There are also fractal communities on many other art sites, and I participate in some of them. If you would like to get support from a fractal art community, go to and use the search term "apophysis". You will get links to a number of groups, and the people are very supportive..

The critically important thing to remember about any computer generated art, fractals in particular, is that a human being DESIGNS them. While some people might just accept what happens by chance, a good fractal artist will shape and sculpt the image and run it through many processes. It is truly human art, even though the paintbrush is a computer.

Thank you to Squidoo and the Squidoo community for the Purple Star and the Lens of the Day! 9/8/13. Also, thank you for all the wonderful support: comments, Squidlikes, etc. I am overwhelmed and I appreciate it very much!


One of the wonderful things that happens as a result of participating in a fractal community is that people help each other. Providing starter files and scripts are both very common. I have received many such gifts from people at deviantART, and I would like to mention them by name. In most cases, I don't know their real names, just the names they use for artistic purposes.

Gateman45 - starter files

Classylady - starter file

Skyfirehead - scripts

Anjaleck - starter files

Cabintom - scripts

justravelin - starter file

fractalangel-stock - starter file

tdierikx - tutorial

Whenever I make use of such a gift, I make very sure that the results look very different from what I received.

A script is some add-on code that provides good starter files (which are generated on request by the computer), or that transforms existing files in a certain way. I have developed one script myself, which I will identify in the images where I used it.

Mandelbrot Set

This is a basic graph of the mathematical formulas that are used to make most fractal art.

A derivative of this is called the Julia, also named after the developer.

Spirals are very, very common in fractal art. The basic characteristic of fractal art is that it is possible to zoom in and enlarge a portion of the image, and you will see new details. The zooming can be continued for a very long time, although eventually the detail degrades.

There are many examples of fractal art in nature. The leaves of trees and ferns, cloud patterns, flowers, and many other things often demonstrate a fractal pattern. It is a very good example of how something which is basically very simple can make a very, very complex image.

Abundant Color

This example shows how spirals are often prominent in fractal art.

The colors are made by what are called gradients. Gradients display as a strip with a number of bands of color across the strip, usually with some black bands. The black bands cause the crispness of the image. Without them or a similar contrasting color, there would be no structure.

There are developed gradients available, and you can generate your own.

This is the entire image from which the detail in my introduction was taken.

Flowers in Her Hair

This image was developed from the same basic parameters as the previous one.

Sand Sculpture

This is an early image, and it really "just happened". The originally generated image looked very similar to this, and I just refined it. Sometimes this kind of serendipity happens. A few of my fractal images were developed in this way.

Tweaking is the process of altering a fractal image to look like you want, before you cause the program to record a set of instructions that will generate the large image. These instructions can be saved. They can also be modified into new works later.

Cactus Wood

This is another early fractal that "just happened". It does somewhat resemble the structure of wood in a cactus skeleton (particularly in cholla), hence, the name.

I went through a lot of schlocky results to find these first few, before I learned how to tweak something that was basically a bunch of junk into something that I found pleasing.


Derived from the same starter as Cactus Wood.

Many Birds

Another early one. The one which follows next was derived from the same starter formula.

Magnificent Flames

Magnificent Flames - detail

Fractals are still a fairly new art form. I am interested in finding out how widely known they are today.

Were you familiar with fractals before reading my lens?

See results

Third Dimension

This is the first of several examples I will show that were made with my own script. The amount of detail in this image is phenomenal.

This is a favorite of Charly Moore, who gives tours of Antelope Canyon and owns the Thunderbird Gallery in Page, Arizona. He named it.

Third Dimension - detail

Here you can see some of the details in this image. Look closely for very fine lines and similar structures.

Purple Spikey

Same starter and script (mine) as the previous fractal.

Rug Weaver

Final example of this series. The name refers to the fact that the colors used are the same ones used by Navajo (Dineh) women who weave rugs.


This one, like the one in my introduction, was made from a starter designed by Anjaleck.

When I first met her, her daughter had just been tragically killed in an auto accident. She is now raising her two granddaughters. Life was rough, but I stood by her as best I could, and we became good friends. It is often the case that friendships formed as the result of fractals and gifts to one another deepen into friendships with many more facets.

This has a lot of detail that is difficult to see here. To see a larger image, visit Aggregates

Aggregates Detail

Here is a portion of the image slightly larger so you can see the details better.

Blue Spiral with Twigs

This image was generated using a spiral batch script by Skyfirehead. A batch script produces several starters at once, and you can work on any of them, or several of them, your choice.

School of Manta Rays

From the same spiral batch script as the previous. The basic shape of each spiral reminded me of a manta ray, and the collection forms a school, even though manta rays don't do that. :)

The spiral was combined with fractal plants, at the bottom, and bubbles, in Paint Shop Pro.


Another image of two combined fractals, put together in Paint Shop Pro.

The triangular pattern in the background represents the Trinity. Superimposed is the cross of Christ. Hence, salvation.

17 - Bird of Paradise

This came from a starter file given to me by Gateman45. He is retired, and makes fractals as a hobby. I'll think of a better name someday...

Thank you to RoadMonkey for the excellent title!

Jewels - Tribute

From the same file as the previous. Of the images I uploaded, I knew this would be Gateman's favorite, so I dedicated it to him. I was right! :)

Copper Techno

I don't remember where I got the original starter for this one. Maybe I'll think of it later.

Time Warp

From the same starter as the previous image.


An early one. Very popular with people.

Organic Tanguy

From a starter by Classylady. Thank you.

Named after Yves Tanguy, a French surrealist painter, because it reminds me of his work.

Jeweled Bubbles Tanguy

From the same starter as the previous.


This is one of my very favorites. I had this one made up as a wall hanging which is 36"x36" and it is stunning!

Impassionate Flames

Another of my very favorite ones.

To see Part 2 of this collection, please visit here: Apophysis Part 2.

Purple Star

Thank you very much for the Purple Star!

Let me know what you think.

Thank you to all of you for the lovely comments you have been leaving me. I deeply appreciate each and every one.


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