How to Simulate Fractals in Photoshop

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Have you ever seen those outstanding fractal images with a lot of swirls and colors? Some of those were build simulating fractals or repeating shapes, where each shape is a reduced part of the whole, others were build mathematically. In this tutorial, we’ll create a stylized fractal design using only Photoshop.

Final Image Preview

Let’s take a look at the image we’ll be creating. Want access to the full PSD files and downloadable copies of every tutorial, including this one? Join Psdtuts+ PLUS for just $19/month. You can view the final image preview below or view a larger version here.

Final Click

Video Tutorial

Our video editor Gavin Steele has created this series of video tutorials to compliment this text + image tutorial.

Step 1

Wikipedia define fractals as "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole." There are many ways to create fractals, most involve complex mathematical formulas, or fractal software programs, like Apohpysis for example, but with our good old Photoshop we can simulate the fractals behavior using repeating shapes and some useful keyboard shortcuts.

So, let’s get it started. First we’ll start with a 1600 pixels by 1200 pixels document, it’s huge because I’m planning to use it as a desktop background. Then, show the ruler (Command + R) and change the unit to Percent. Now, draw two guides, one horizontal and the other vertical, and place them in the middle of the document. Next, using the Gradient Fill Tool, draw a radial gradient (#095261 – #000000), which should look similar to the image below.

Step 2

Now here’s the only shape you’ll draw: a circle, yes I’m not kidding, everything starts from a single circle. Draw it using the Ellipse Tool, hold the Shift key to create a perfect circle, and if you want hold the Alt key to draw it from the center. The circle size is 83 pixels by 83 pixels and it’s located in the middle of the document. Now, create a new folder named "Fractal" and place the circle shape inside of it.

Step 3

Let’s add some depth and volume to our shape. First, apply a Gradient Overlay that goes from dark blue to light blue, with a Drop Shadow, 50% Opacity, and a 0px distance, some Bevel and Emboss, including a texture. Just follow the images below.

Step 4

Now duplicate the circle layer by dragging the shape while pressing the Alt key, then merge the circle copy with a new blank layer to keep the style proportional. Resize the copy a little bit and place it 120 degrees from the middle of the document, you can use a triangle as a guide (I drew the triangle using the Polygon Tool).

Place the copy just over one of it’s corners. Repeat this twice to get three small circles around the big circle. Delete the triangle and finally merge the four circles into a new layer called "Fractal 1" (If you want leave a copy of the original vector shape just in case).

Step 5

Here comes the fun part, we’re going to repeat two steps several times. This is the first one, we’ll Duplicate and then Free Transform. To get the right effect we need to use the shortcut Command + Alt + T. This command duplicates the existing image and allows to free transform the copy. Do not click anywhere and go to next step.

Step 6

While holding the Shift key, resize the "Fractal 1 copy" just a little bit, then rotate the copy a few degrees Clockwise. The trick to simulate the fractals is move the Transform center to the left, right, top, or bottom, depending on your needs. This time we’ll move it a lot left. Finally, hit Enter.

Step 7

Now we’re going to use another useful keyboard shortcut. Press Command + Shift + Alt + T to apply Free Transform again once and see the result. What happened? Photoshop takes the previous values of the Free Transform and apply them to the new object. If you repeat this command several times you’ll get a nice fractal swirl. Photoshop creates a new layer each time you apply this command.

Step 8

Now, duplicate the entire "Fractal 1" folder, then select the "Fractal 1 copy" folder and hit Command E to merge the group. Now name the resulting layer "Fractal 2", then hide the original folder. Also, move the "Fractal 2" layer some pixels down and to the right from the middle of the document.

Step 9

Select the "Fractal 2" layer, then apply the Duplicate and Free Transform keyboard shortcut from Step 5 (Command + Alt + T), though change the transformation center to the middle of the document and rotate the image -120 degrees CCW.

Step 10

Now hit the Free Transform again keyboard shortcut from Step 7 (Command + Shift + Alt + T), doing this you’ll duplicate the 120 degrees rotate transformation exactly. Finally, put the three layers into a new folder named "Fractal 2," Now, duplicate the folder and merge the copy, hide the original folder, and name the merged copy "Fractal 2."

Step 11

Duplicate and Free Transform (Command + Alt + T) the "Fractal 2" layer, keep the transformation center where it is, then while holding Shift + Alt keys, resize and rotate the copy just a little bit. Try to get something like the image below.

Step 12

Change the "Fractal 2 copy" layer Hue/Saturation, use the values shown below. We’ll make this one a little bit green.

Step 13

Free Transform again the layer and adjust Hue / Saturation using these values.

Step 14

Repeat the Free Transform again command (Command + Shift + Alt + T) as many times as you want, but always change the Hue and Saturation to get one green layer above a blue one. When you have finished, group all the layers into a new folder called "Fractal 3." Next, duplicate the folder and merge the copy, just like in the previous steps. Name the copy "Fractal 3."

Step 15

Add a dark Drop Shadow to the "Fractal 3" layer.

Step 16

Duplicate and Free Transform (Command + Alt + T) the "Fractal 3" layer, rotate the copy a few degrees CW, resize it a little bit making the copy smaller, and change the transformation center to the top-left, then hit Enter.

Step 17

Free Transform again (Command + Shift + Alt + T) a lot of times to get something like this. You can repeat these steps as many times as you want, but I’ll stop the design right here.

Conclusion

As you can see, you can apply this technique to create a lot of abstract designs, or mixing the fractal shapes with real images to improve your outcome. It’s up to you from here. Good luck! You can view the final image below or view a larger version here.

Final Click

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Discussion 130 Comments

Comment Page 3 of 3 1 2 3
  1. John says:

    Nicely done, “How to Cheat in Photoshop” by Caplin, he explains this and much more.

  2. Allegra Ricci says:

    I will try this fantastic work. Thanks to explain us with this tutorial.

  3. Allegra Ricci says:

    Is really cool work, thank you!

  4. Thank you so much for sharing your work with me. I really appreciate it and you did such a great job of making the step by step process easily understandable! I’ve favourited your blog too! Awesome to have such a great resource handy.

  5. Alex says:

    Beautiful… however after completion of this tutorial my computer committed suicide…

  6. madoo says:

    this is agreat idea to drawing thank u alot

  7. anr says:

    great tutorial, it took me a while to understand some things, but the whole idea is just great, i even didn’t knew about this ctrl+alt+shift+t thing, it’s just the same as in illustrator.

  8. Jack says:

    Brilliant tutorial, easy to follow if you know the very basics of photoshop, brilliant man

  9. Nichole says:

    For those of you griping about this being an “old tut”, I have a newsflash for you… some of us weren’t around in the dinosaur era so we weren’t able to experience this before. If you don’t want to see the tut again, DON’T LOOK FOR IT. You know the only reason you did was so you can gripe about it.

    For those of your saying it’s stupid, grow up.

    For those of you bitching that it’s a shame it’s for tutsPlus members, get a job and buy a membership, support a cool site.

    This guy did a nice job, and whether he’s reposting something from before or not, his tut deserves some respect. After all, it looks like plenty of people found this to be a good tutorial.

    So seriously, shut it with the negativity.

  10. yash says:

    is very good tanx

  11. yash says:

    is very good work & nice thanku

  12. evilkitty75 says:

    WOW this is amazing i just had a try n didnt realize it was so easy
    thankyou for this kinda ‘never endin’style of work i love it!!!! XXXX XX

  13. Neetu says:

    Amazing work A Great WOW!

  14. Kresna says:

    this is beautiful, especially when applied with batik from indonesia….!!!!!! many thaaaaankss!!

  15. Loved it! Looks really pretty!

  16. Sinduja says:

    AWESOME Tutorial…

    Great for Learners…

    My FIRST Project in Photoshop and thanks to you I got it Perfectly !!!

  17. Omar Faruk says:

    Sir, I really like your works. Thank you from my heart as nothing more than thanks.

  18. Eanas says:

    درس رائع جدا

  19. katarina says:

    Thanks so much! I learned some nice tricks thanx to You:)

  20. Muito obrigado por esse belissimo tutorial
    cada dia aprendo mais com vocês.
    Abraços

    My version: http://felipegenuino.com/blog/portfolio/fractals/

  21. RC says:

    It’s tutorials like this that really worry me in that they show how dependent Photoshop users are on the program, almost to the point where they don’t realize their options anymore. There’s absolutely no need to go through the trouble of “simulating fractals” in Photoshop when you can create real ones using one of a number of great commercial and freeware apps. There are even plugins for Photoshop to create fractals.

    And Nichole, there’s really no need for your nasty attitude. The other poster was correct: it’s kind of lame to simulate something that can easily be done using a bevy of other options. Instead of being such a fanboy and reacting to differing opinions with such hostility, open your horizons. Photoshop is a great program but it also isn’t the end and be all to the level where it can do everything. That is what the other poster was trying to say. If you want to force Photoshop to do everything– even to “fake” those things better left for a more specialized program– be my guest. But by relying so heavily on Photoshop like that you limit yourself as an illustrator. Every Photoshop fanboy who follows this “fractal” tutorial will create the same type of fractal illustration with little variation. But a person who uses fractal software can create a near infinite number of graphics that each look radically different. Which one do you want to be? The former or the latter?

  22. Hogarth says:

    Good job man!It’s perfect!Thank you so much!

  23. sman says:

    I have no ever seen like this to make a fractal!!!

  24. wagster says:

    I have to disagree with you there, RC. This tutorial is not about simulating fractals (whatever it may say), but about creating them. It teaches you to create something that is self-similar regardless of scale – which is the definition of a fractal.

    I’ve used (and written) a number of applications for rendering Mandelbrot/Julia sets as well as a few other oddities like Newton’s method. It’s fascinating and addictive, but not very useful when it comes to commercial design. All you can really do is recolour them or wrap them around 3D objects. Mathematically derived fractals were hugely overused in the 90′s and I wouldn’t try and use them in client work these days.

    This tutorial opens up a new new option for design, I just think it’s a shame that the Alvaro opted to try and replicate an arm of the Mandelbrot set rather than create an abstract fractal based on a random image, just to see what happened.

    My 2c worth.

  25. cucnguyen says:

    it;s amazing work. thanks for simple but nice tut

  26. Maggi Blair says:

    As someone fairly new to photoshop and also UltraFractal, I’m well impressed with this tut and I can see lots of uses for it as a stand-alone tut and as a finisher for some rendered fractal images. Excellent.

  27. matty686 says:

    @ RC

    I have based my whole career as an artist around this method and I don’t appreciate it being insulted

    there are all kinds of variations you can do you can enforce symmetry you can warp things you can re use old parts I post my fractals on fractal forums and I am well appreciated to tell you the truth i have i was actually told i brought something exiting to the field

    these fractals come out the way you imagine you have full control if you don’t like that it’s not for you

    if you need open-source use ink-scape with the extract to gimp feature and no i dont press transform again i have evolved far beyond that to a repetitive class like system with re used image parts
    and no i don’t program anything i just construct
    you can check out my art at

    http://www.fractalforums.com/index.php?action=gallery;sa=view;id=3552

    http://www.fractalforums.com/index.php?action=gallery;sa=view;id=3485

    http://www.fractalforums.com/index.php?action=gallery;sa=view;id=6103

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