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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.

Guestbook Comments - Critiques allowed. :)

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    • Pat Goltz profile imageAUTHOR

      Pat Goltz 

      5 years ago

      @Cari Kay 11: Thank you! They are fulfilling their purpose.

    • Cari Kay 11 profile image


      5 years ago

      I find such beauty in these!

    • Stephanie36 profile image


      5 years ago from Canada

      These are so cool! I can't draw very well, either. I'd love to try these one day. :)

    • ChalhoubCassidy profile image


      5 years ago

      Very cool.. who knew mathematics could translate into art. Great visual

    • profile image


      5 years ago

      Hauntingly Beautiful imagery in a stunning artistic lens! You have an enviable talent and an incredible eye! Fractals rarely come along that are more beautiful than these! Thank you SO much!

    • Bercton1 profile image


      5 years ago

      Great collection and brilliant blend of colors!

    • Pat Goltz profile imageAUTHOR

      Pat Goltz 

      5 years ago

      @Uzuki Gems: Why, thank you for those kind words! There's a lot of fractal schlock out there. But it can be very nice if a person is truly skilled, and I know a few truly skilled fractal artists.

    • Uzuki Gems profile image

      Uzuki Gems 

      5 years ago

      Such beautiful pieces! Fractal art is now officially my favorite kind :)

    • graysquidooer profile image


      5 years ago

      I had never heard of Fractal images, until I read your wonderful lens

      The actual images are really beautiful too, congratulations on this lens

    • Pat Goltz profile imageAUTHOR

      Pat Goltz 

      5 years ago

      @smine27: You're welcome, and thank you for the kind comment.

    • smine27 profile image

      Shinichi Mine 

      5 years ago from Tokyo, Japan

      Such beautiful examples of fractal art. I never knew they could look so beautiful. This lens gave me a sense of appreciation for them. Thank you.

    • profile image


      5 years ago

      Omg! These are gorgeous! I had never heard of fractals before... these look like something from another dimension! Wow...I learned something new today.....

    • LisaMarieGabriel profile image

      Lisa Marie Gabriel 

      5 years ago from United Kingdom

      I find these pieces really interesting. I have seen the Mandelbrot fractals in, but was never sure what to do with them. I love the "aggregate" one!

    • Pat Goltz profile imageAUTHOR

      Pat Goltz 

      5 years ago

      @Aladdins Cave: Ta heaps!

    • Aladdins Cave profile image

      Aladdins Cave 

      5 years ago from Melbourne, Australia


      The Copper Techno was best.


      Cheers from DOWNUNDER

    • kingsrookie lm profile image

      kingsrookie lm 

      5 years ago

      Amazing pictures. I studied fractals in school and was always fascinated. Crazy how some fractals can be found in nature but you took them and made them art!

    • SavioC profile image


      5 years ago

      This is amazing stuff. I never heard of them earlier this just blew my mind. In college I tried doing graphics using the age old program BASIC. Superb.

    • Pat Goltz profile imageAUTHOR

      Pat Goltz 

      5 years ago

      @Lee Hansen: Thank you. I first used CompuServe and then FidoNet. I'll check out your honor roll.

    • Pat Goltz profile imageAUTHOR

      Pat Goltz 

      5 years ago

      @Mommie-Moola: I don't know if you have ever seen the structured fluid videos on YouTube. Maybe like one of those, but colored white. :)

    • Mommie-Moola profile image


      5 years ago

      I wonder what fractal milk would look like?? ;)

    • Lee Hansen profile image

      Lee Hansen 

      5 years ago from Vermont

      Wow, fabulous fractal art! I confess I remember the I Like Ike campaign and the first polio vaccination clinics. My first online access at home was via CompuServe although I used email and file transfer via DECnet and ArpaNet years prior to that ... I've added this great art lens and award winner to my Purple Star Pastiche honor roll - feel free to visit and vote for it/share your inclusion.

    • Diana Wenzel profile image

      Renaissance Woman 

      5 years ago from Colorado

      Totally mesmerizing. Exquisite. Stunning fractals. Congratulations on your honors. I know you worked hard to get to this level of accomplishment. Quite a gift you have as presented here. I would like to experiment with fractals. I think it would be very stimulating.

    • profile image


      5 years ago

      Really Awesome!

      Great lens

    • bobnolley lm profile image

      bobnolley lm 

      5 years ago

      Absolutely wonderful stuff! Congrats on the purple star, indeed!

    • Pat Goltz profile imageAUTHOR

      Pat Goltz 

      5 years ago

      @PlumberJorge: Thank you! Those are words of high praise.

    • PlumberJorge profile image


      5 years ago

      Incredible lens!. Congrats on the purple star!

    • VspaBotanicals profile image


      5 years ago

      Really beautiful!

    • LoriBeninger profile image


      5 years ago

      Beautiful. I had no idea...

    • tricksplace profile image


      5 years ago

      Very cool fractals!

    • profile image


      5 years ago

      Incredible! Fractal art is new to me, so I'm speechless.

    • Pat Goltz profile imageAUTHOR

      Pat Goltz 

      6 years ago

      @FrancesWrites: Thank you! And I'm all for looking out of the window of the TARDIS. :) WHO suggested that.

    • FrancesWrites profile image


      6 years ago

      I've seen a good deal of fractal art, and I love it because the variations in it are so individual. Blue Spiral with Twigs and Bird of Paradise for example are so delicate and filmy, feathering away at the outer edges, yet Copper Techno is solid and industrial. Brilliant is sort of what I think it would look like if you looked out the window of the TARDIS in flight :) Lovely work and a delightful lens - congratulations on LotD and your Purple Star :)

    • mcstacy profile image


      6 years ago

      I've read some of your other lenses about fractal art. Your fractals are so beautiful. I hope to give a try in the near future. Thanks for sharing.

    • marie-churchman profile image


      6 years ago

      Beautiful! I feel so inspired. I've never tried fractals, but I want to now. Your a wonderful artist.

    • mel-kav profile image


      6 years ago

      Wow! These fractals are amazing! I thoroughly enjoyed this lens. You are very talented.

    • profile image


      6 years ago

      omygosh, I am having fun but truly amazed at what you have done!! I am trying things out, but anxious to learn more about how the math works to make the designs. denise evans

    • profile image


      6 years ago

      Wow those pictures are cool! Been in photography and digital photography but I didn't know that you can make those ;)

    • Gloriousconfusion profile image

      Diana Grant 

      6 years ago from United Kingdom

      I've tried simple fractals, but nothing like this - your work is fantastic and plenty to learn here

    • Pat Goltz profile imageAUTHOR

      Pat Goltz 

      6 years ago

      @MariaMontgomery: Thanks so much!

    • MariaMontgomery profile image


      6 years ago from Central Florida, USA

      Congrats on the LOTD! I just got my first one a little over a week ago. This is a beautiful lens. I've learned about a type of art I don't really understand, but plan to explore.

    • profile image


      6 years ago

      Nice pictures! Art is a hard passion every one can't do this.

    • Pat Goltz profile imageAUTHOR

      Pat Goltz 

      6 years ago

      @DebMartin: Of course, if you examine a lot of plants (and other things, for that matter), you see that they ARE fractal-designed.

    • profile image


      6 years ago

      Beautiful. It's amazing how something computer-generated can look so organic.

    • Gayle Dowell profile image

      Gayle Dowell 

      6 years ago from Kansas

      I am amazed at how art is so easily integrated into other subjects. Math being one of those subjects. Just goes to show that beauty can be found everywhere.

    • profile image


      6 years ago

      Awesome pictures. I loved watching them.

      Great Job

    • weakbond profile image

      Nnadi bonaventure Chima 

      6 years ago from Johanesburg

      Nice lens and beautiful pictures , thanks for sharing

    • profile image


      6 years ago

      I love fractals and these are all amazingly awesome! I've tried to make a few but haven't taken the time to really learn it. Thanks for sharing it.

    • Minoru10 profile image

      Michael Yoshinaka 

      6 years ago from Honolulu, Hawaii

      Looks so complicated to do seems so easy with the use of computers.

    • Vortrek Grafix profile image

      Vortrek Grafix 

      6 years ago

      Very cool!

    • CharMarie profile image


      6 years ago

      Awesome images! I've never heard of this before your lens! Interesting! Thanks for sharing!

    • MrAusAdventure profile image


      6 years ago from Gold Coast, Australia

      Wow! I have never heard of these types of images before but they look pretty cool. Amazing what you can do with computers these days, even for those of us who are not very artistic! Congrats on LOTD. :-)

    • CrazyHomemaker profile image


      6 years ago

      This is so cool!!! I've never heard of or seen fractal images before. They are beautiful. I'll have to start checking this out. Congrats on LOTD and Purple Star.

    • ElaineMarlowe LM profile image

      ElaineMarlowe LM 

      6 years ago

      What beautiful art, I don't know that I have ever seen anything like it. And bravo for a wonderful lens.

      Selah, Elaine

    • Pat Goltz profile imageAUTHOR

      Pat Goltz 

      6 years ago

      @buteoflyer2: First suggestion is to play with the program for awhile. Try the different controls, and learn their names. Then the tutorials will make more sense. Also collect starter files and scripts, and try them. Scripts are a huge part of the solution, and it takes awhile to learn to write them, but the fractal community has been very generous to share scripts and some of them are excellent.

    • profile image


      6 years ago

      Superb selection of fractals. Congratulations on getting LotD and the Purple Star!

    • archetekt lm profile image

      archetekt lm 

      6 years ago

      What beautiful images! I'd never seen this type of art before, or maybe had but didn't know what it was. I think School of Manta Rays is my favorite.

    • profile image


      6 years ago

      Fractals are such naturally beautiful images. Thanks for sharing.

    • buteoflyer2 profile image

      Kathie Miller 

      6 years ago from Southern California

      I've been fascinated with fractals for some time, but have never got into it much. You mention fractal communities, but don't mention any. Do you have a few favorites for a complete novice to join? I downloaded the Apophysis, but all the tutorials are either completely Greek to me, or are no longer available. Where would you suggest I go to get started?

    • RaintreeAnnie profile image


      6 years ago from UK

      These are really so very beautiful. Congratulations on LOTD!

    • MartiLawrence profile image

      Marti Lawrence 

      6 years ago from Grain Valley, Missouri

      Stunningly beautiful! Thank you for teaching me about these.

    • jupiter justice profile image

      Asher Socrates 

      6 years ago from Los Angeles, CA

      These are very addictive once you get the hang of designing them. Great lens on Flame Fractals. Thanks Asher

    • flinnie lm profile image

      Gloria Freeman 

      6 years ago from Alabama USA

      Love this it's so amazing.Thnks for sharing this with us. Congrats on LOTD.

    • profile image


      6 years ago

      Just read about fractals in The Shack; had NO idea of what they look like. Your art is simply, and Divinely, beautiful, especially since it has a math source- never my fave subject!

    • LotusLandry profile image


      6 years ago from Southern California

      I've experimented with samples of Java software code for classic fractals loaded into NetBeans.

    • profile image


      6 years ago

      Beautiful! Math is amazing. I sent this to my mom who is really into fractals and other mathematical imagery.

    • Nancy Hardin profile image

      Nancy Carol Brown Hardin 

      6 years ago from Las Vegas, NV

      Lovely work, and congratulations on LOTD. Well done!

    • RoadMonkey profile image


      6 years ago

      Beautiful. I love fractals and these are some really stunning examples. I think your "#17" is a "Bird of paradise".

    • profile image


      6 years ago

      Very beautiful designs. truly amazing

    • Steph Tietjen profile image

      Stephanie Tietjen 

      6 years ago from Albuquerque, New Mexico

      I love these images--your colors are wonderful. Too bad the software is not available for Macs.

    • profile image


      6 years ago

      Love these, they are all so perfect, each one is!

    • profile image


      6 years ago

      Totally awesome, loved it, big congratulations on your Lens of the Day! Wow, I could look at these images for hours!

    • delia-delia profile image


      6 years ago

      Congratulations on LOTD! AWESOME IMAGES and lens!

    • profile image


      6 years ago

      Ah, I would say this is rather like analytical art - quite colorful and inspiring!

    • profile image


      6 years ago

      Beautiful works of art! You are talented...

    • profile image


      6 years ago

      What an experience! Hypnotizing. State changing. Focusing on the image alters reality.... Uh...I'm going to get more coffee and get back to my writing....oh, and congratulations on LOTD...

    • esmonaco profile image

      Eugene Samuel Monaco 

      6 years ago from Lakewood New York

      I have never hear of this at all Thanks for sharing this, this is what I love about squidoo I learn something new almost every day Thanks Again

    • David3142 profile image


      6 years ago from West Midlands, England

      Beautiful images and all made with maths!. Thanks for sharing.

    • rubylinz profile image


      6 years ago

      Gorgeous lens! Thank you! I have always been interested in fractals.

    • profile image


      6 years ago

      this is great to see, thanks for sharing your work, and making such an educational lens.

    • profile image


      6 years ago

      These fractals images are really beautiful, interesting to look at too.

    • Faye Rutledge profile image

      Faye Rutledge 

      6 years ago from Concord VA

      Amazing! Congratulations on LotD! :)

    • profile image

      Dave Franklin 

      6 years ago

      absolutely mind blowing stuff, thank you for sharing

    • Pat Goltz profile imageAUTHOR

      Pat Goltz 

      6 years ago

      @anonymous: Yes, I have been using Ultrafractal for over a decade. In another one of my lenses on fractals, I present images from this program. Thank you for the kind comment!

    • profile image


      6 years ago

      This is just Amazing.. I never knew an art of this sort existed.. :) love it!

    • profile image


      6 years ago

      very nice, great, and ........... lens! wow

    • profile image


      6 years ago

      lovely images and educational for me. thanks

    • BobZau profile image

      Bob Zau 

      6 years ago

      These are some beautiful images... well done!

    • Susan Zutautas profile image

      Susan Zutautas 

      6 years ago from Ontario, Canada

      Beautiful work!

    • PippiDust profile image


      6 years ago

      These are beautiful. I'll download Apophysis and try to make it myself too. And congratulations for Lens of the Day.

    • profile image


      6 years ago

      Your fractal work is beautiful! Have you ever tried UltraFractal? It's not free but you might enjoy working with it.

    • Pat Goltz profile imageAUTHOR

      Pat Goltz 

      6 years ago

      @girlfriendfactory: It takes a lot of practice to make images like this, and beginners are often discouraged by the results they get. It is also important to learn from the fractal art community. I can't claim sole credit for my images, because I got a lot of help from other people.

    • profile image


      6 years ago

      nice,this art form is very good

    • profile image


      6 years ago

      Great photos enjoyed reading your lens

    • girlfriendfactory profile image


      6 years ago

      Lovely! I've never created fractals but I may try someday if they turn out this good! :-)

    • rattie lm profile image

      rattie lm 

      6 years ago

      Just delightful. Thanks so much for sharing.

    • JenaleeMortensen profile image


      6 years ago

      Apophysis is a great way to make fractal art designs.

    • profile image


      6 years ago

      wows, very pretty picture. i am try to create this art at this time.

    • stephaniehut profile image

      Ice Blue 

      6 years ago from Port St. Lucie

      These pictures are soo pretty!!

      I never knew about that kind of art, until I read your lense

    • mcsburlea profile image


      6 years ago

      these images are gorgeous

    • edsplace profile image


      6 years ago

      First time experience with Fractals. Fascinating way of displaying art. Very cool. Thanks :)


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