Fractal Art: How to Create Basic Fractal Flowers in Apophysis

What You'll Be Creating

The basic fractal flower needs only two total transforms. With practice you will be able to create a wide variety of unique and fun fractal flowers using this technique. I'm using specific numbers for the weights and variations so that you are able to reproduce the results exactly and gain a working knowledge of how these flowers are created. You should feel free to experiment with the values after you have worked through the tutorial.

1. Set the Stage

Step 1

Begin by opening the Editor window in Apophysis and choosing the New flame option to reset to a blank screen.

Step 2

Remove linear from the transform on the Variations tab by changing it to 0. Set the spherical variation to 1.

2. Setting Up the Two Base Transforms

Step 1

Move this first transform up 0.5 units and to the right 0.2 units. The easiest way to accomplish this is to switch to the Triangle tab and set the units to 0.1. Then use the up arrow five times and the right arrow twice. This will allow you to maintain precision until you begin to adjust this transform by hand.

Step 2

Now we need to rotate the transform by 105 degrees. To do this, change the degrees of rotation from 15 to 105 and click the Rotate clockwise button.

Step 3

Before we move on to the next transform, let's modify the weight of this spherical transform slightly. We want Apophysis to focus more on this transform than the next. The default weight for all new transforms is 0.5. Change the Weight on Transform 1 to 0.75.

Step 4

Create a new transform by clicking on the New transform button at the top of the Editor's toolbar.

Step 5

Before we move this transform, let's modify the variations applied to it. Currently linear is set to 1. Switch to the Variations tab and change linear to something around 0.55. You can modify this value later to see how it changes the effect. Additionally, add in radial blur with a value of 0.45.

Step 6

Modify the Weight of Transform 2 to 0.23.

3. Finer Positioning of the Transforms

Step 1

The next few steps can be a bit tricky, so keep your eye on the variation preview window on the top right-hand side of the Editor to see how the fractal is being affected by the changes you make. Change to the Triangle tab. Use the smaller triangle in the Editor to decrease the size of the triangle by 125. Do this a total of seven times. Each time you click the triangle to reduce the size, notice how the shape of the fractal is beginning to form.

Step 2

This adjustment could be done with great precision in the Editor text boxes, but we are going to do it by hand to gain a better understanding of the effects a transform has on a fractal.

Click on the Y-axis of the second transform. It will be the yellow circle node with the Y beside it. Drag this node down and to the left so that you stretch the triangle and flatten it out.

Step 3

Going back to your Editor tools on the Triangle tab, move Transform 2 to the right by 0.6 units.

Step 4

Rotate Transform 2 clockwise by 105 degrees. This action gives us the structure of the petals. Switch to the Variables tab and change the radial_blur_angle to 0.2444. This adjustment affects the shape of the petal.

4. Setting Up the Colors

Step 1

Before we finish up the structure of the fractal, let's adjust the colors. In the Adjustments panel, choose the Gradient tab and select the gradient 100_rw_yellow_orange.

Step 2

Switch back to the Editor and this time the Colors tab for Transform 2. Change the Transform color number from 0.0 to 1.0. Adjust the Color speed to somewhere around 0.015.

Step 3

Make Transform 1 active. Change the Color speed setting to about 0.66. Drag along the Transform color slider until you find a color combination you like. Feel free to adjust the Color speed as well.

5. Bringing It All Together

Step 1

If you're still with me, so far it looks as if all we have created is a big mess. That is about to change. Make certain Transform 1 is still active. In the toolbar of the Editor, click the Flip horizontal button. This button looks like two tall triangles side by side. Notice the transformation!

Step 2

Now we're really seeing all of this hard work pay off. This step requires finesse and patience. The origin of each transform is a node labeled with a capital O. You can click on this node and drag the entire transform around the plane. Try it now, and as you do, observe the amazing transformation of the fractal. Take your time and try to find a nice flower design.

Step 3

Once you find a flower shape you're satisfied with, close the Editor window. In the main window, use the zoom and positioning tools to focus on a particular part of the flower and give more visual interest and presentation to your fractal. A tool in the toolbar called Show guidelines will allow you to visualize the rule of threes.

6. Final Adjustments

Your fractal may appear to be dark, as mine does in the above image. You can easily correct lighting issues with the Adjustment panel.

Inside the adjustment panel, switch to the Rendering tab. Here you can adjust the amount of gamma (in this case pixel depth) and the brightness of the fractal. At times, the main window of Apophysis will mislead you with regard to brightness. Trust the smaller preview window in the Adjustment panel when you notice discrepancies.

If we render this fractal now (feel free to test it out), you will notice an extreme amount of “fractal dust” in some images. This can be desirable at times, but in this particular case, it looks as if we do not know what we're doing and we've just created a mess.

Let's remedy that by lowering the Gamma setting down to 1.2. This reduces the total amount of pixel depth. Next, change your Brightness setting to somewhere between 1.2 and 3. This style of fractal is naturally bright and reflective, so too much brightness will easily lead to the whites being blown out.

7. Rendering the Fractal

The last step is to render the fractal. Click the purple gear on the toolbar of the main window to access the rendering interface. Here you will want to adjust several options, including where to save your fractal image and at what size you wish to render it.

Keep in mind that large renders can take several hours to days to complete. Also bear in mind that you can choose a jpg image extension to have a solid background when saving your image, or select the png format for a transparent background.

Set the Density to 10,000. Change Filter Radius to 1. This will render a very smooth fractal. If you want more crisp edges, lower this value to 0.5, or feel free to experiment with other settings.

The Oversample setting will render the fractal at the size you have chosen, multiplied by its number, and then downsize the image automatically to create a smoother image overall. In our case, rendering the fractal at 600 pixels wide with an oversample of 3 means that Apophysis will render the fractal internally at 1800 pixels wide and then downsize it automatically. In this instance, an oversample of 3 is very useful. Don't go crazy with the oversample setting, as it requires exponentially more RAM and is rarely useful above the value of 3. For some very large renders, I only use an oversample of 1.

Below are a few different renders I created by modifying values and dragging the spherical transform around in the Editor. Try experimenting by modifying the values of the variations on both transforms. Adjust the weights to see how it affects the overall image. Move both transforms around and rotate them to discover more combinations and some incredible effects. Above all, have fun!

Taking It One Step Further

To make the flower above, I added the crackle variation to the radial blur/linear transform. In addition, I changed several values on crackle to create a small blurred effect. Try adding other variations to the linear/radial blur transform to create some interesting structures.

I created the above piece by modifying the radial blur value and adding in a Curl3D final transform. I then modified the values for Curl3D and repositioned the scene. Try adding in different final transforms to see powerful affects on the fractal.

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Fractal Art: Create a Tile Fractal in Apophysis

What You'll Be Creating

This tutorial will equip you with the skills to create a style of fractal known as tiles. The concept of a tile (think subway tile or kitchen backsplash) is ideal for a fractal application because of the repeating pattern of self-similarity. In this tutorial we will explore the power of post-transforms, learn how to apply a final transform, and explore different formulas known as variations within the Apophysis program.

Explanation of Tiles

The fractal tile style comes in a wide variety of shapes, from squares to hexagons and beyond. All of them follow the same basic ideas to create a pattern. Once you've conquered the structure for a tile, the possibilities are literally endless, with a whole plethora of fun formulas to be added and shapes to explore. Today we will focus our attention on the basic square tile.

1. Basic Structure of a Square Tile

Step 1

To begin creating the structure for our square-tiled fractal, open the Editor and click the button for a New/blank flame.

Step 2

The next step is to set up the first transform. We do this because it will serve as a template for the rest of the tile structure. Setting up this one transform and copying it saves us a lot of time and work, and is also good practice because it prevents us from making easy mistakes by forgetting steps or mistyping values.
We will leave the Variation set to linear=1 as the linear formula is the backbone of this type of tile. Change the Weight of Transform 1 to 10. On the Colors tab, set the Color Speed setting to 1. The effect of this will not be apparent right now, but will become evident as we continue.

Step 3

Finally, we need to move this initial transform into place. Move Transform 1 left one unit. Move this same transform up one unit.

Step 4

Now that the first piece of our tile is in place, we can create the rest of the tile structure. Each of these transforms will be a duplicate of the first transform we setup.
Duplicate Transform 1 by clicking the Duplicate Transform button at the top of the editor. Move this transform to the right by two units.

Step 5

Duplicate Transform 2 by clicking the Duplicate Transform button. Move Transform 3 down by two units.

Step 6

Lastly, Duplicate Transform 3. Move this transform to the left by two units.

This completes the basic structure of a square tile.

2. Add the First Shape

The number of options for putting shapes into fractal tiles is staggering. For this tutorial, we'll look at a few different variations and how they can be used to create some amazing artwork.

Step 1

Create a New Transform.

Step 2

At this point, it is good to have the variation preview turned on in the editor. This allows us to see what the particular variation is doing on the fractal plane. It also allows you to visualize what each transform's effect is on the fractal and can provide invaluable information as you design your own fractals.
Right-click in the grid-portion of the editor window and choose the option Show variation preview.

Step 3

For this transform, we need to use the Variations tab of the editor. Remove the 1 from Linear by changing it to a 0. You should now see many small dots in the preview window. This shows you the structure of the tile we set up. To get an even clearer picture, scroll down to find the Blur variation and add 0.5 to Transform 5. You will see the dots become clearer. Change the Blur value back to 0 to continue.

Step 4

To begin adding some shape to our tile structure, find the variation Bubble and change the 0 to 1.

Step 5

At this point, the Bubble variation is too big to be useful in our tile. We could reduce the amount of the variation to 0.25 or perhaps even smaller. However, by doing so, we reduce the affect of the variation, which is not what we're aiming for as it will affect the shape.
Instead we are going to force the transform to become smaller and at the same time retain the round shape of the Bubble variation when set to 1. This is an incredibly powerful technique that will allow you to retain the shape of a variation known as post-transform. This is an over-simplified explanation, but use it to your advantage: when you activate the post-transform, you keep the original shape and can move it at will.
To activate the post-transform mode, look for the button in the top menu bar of the editor that has a Px and a triangle. Click this button to enter the post-transform editing mode.

Step 6

With the post-transform mode active, switch to the Triangle tab. We want to shrink the size of Transform 5. Change the value in the Scale Box (the one with a triangle on either side) to 200. Click the Scale Down Triangle twice.

Step 7

We can edit the shape of this transform more by deactivating the post-transform mode and then scaling down the transform two more times by 200.

Step 8

The next step is to add more structure. Create a New Transform. Remove the Linear variation by changing it to 0. Add Cylinder to this transform by changing its value to 1. The cylinder variation will give a long bar or tube shape.

Step 8

Once again, at a value of 1, the cylinder transform is too large to fit nicely into our tile. It needs to be scaled down just as the bubble transform was. Enable post-transform mode, and scale down Transform 6 by the value of 200 three times. In the preview window, you'll now see the circles from the bubble transform appear connected by a long bar which is our cylinder transform.

Step 9

Let's modify this transform some more. With post-transform mode still active, move Transform 6 to the left 0.5 units and up 0.5 units. Rotate this transform 45 degrees counter-clockwise. Notice that each time we modify the position of this transform, the shape does not change, only the position. This is the power behind the post-transform mode. If we were to perform these same actions with post-transform turned off, the entire shape of the fractal would change drastically.

Step 10

We can get more shape out of this transform by one more trick. Turn post-transform mode off, and scale down this transform by 200 once. This technique will put more texture into the transform and give us a more 3D appearance.

Step 11

To frame out the rest of our shapes, duplicate Transform 6. Enable post-transform mode once again. This time, rotate Transform 7 90 degrees clockwise and move it one unit to the right.

3. Creating a More Complex Structure

Step 1

We've now completed a very basic tile structure and shape. Add a New Transform and remove the linear variation from this transform by changing Linear from 1 to 0. Change the values of Juliascope in the Variations tab from 0 to 1. Enable the post-transform mode and scale down by 200 and then again by 125. Move this transform up one unit. Finally, switch to the Variables tab and change the juliascope_power to 2 and juliascope_dist to 1. These modifications really fill in the rest of the fractal and give it a solid and powerful appearance.

Step 2

Now is a good time to adjust the weights of transforms. Originally we set the weight of the first four transforms to 10. This allows the structure of the tile to hold despite how many more additional transforms we add, allowing us to continue to see what the tile looks like while we design it.
Change the weight of the transforms to the following:

• Transform 5: Bubble: 2
• Transforms 6 and 7: Cylinder: 3
• Transform 8: Juliascope: 3

Notice how changing these weights affects the overall appearance of the fractal. You may also notice a few annoying bright spots near the middle of the fractal. (This will depend on your current gradient). Let's fix those now.

Step 3

Switch to the Colors tab. For each of the transforms 5 through 8, change the Opacity value from 1 to 0. Pay careful attention to the preview window as you make each change and notice how the bright spot changes to conform to the same color values as the rest of the fractal.

Step 4

This is a good time for us to pick a color palette for the finished fractal. Close the Editor and open the Gradient selection window. Choose gradient 558_Explosion.

Step 5

Close out of the gradient selection and open the Editor window. Open the Colors tab. Remember when we set each of the linear transforms to a color speed of 1? We did this so that all of the color changes we make now will be consistent across the entire fractal.
Make the following changes to each of the transforms:

• Transform 5: Transform Color: 0.150 and Color Speed: -1
• Transform 6 and 7: Transform Color: 0.708 and Color Speed: -1
• Transform 8: Transform Color: 0.608

To give more prominence to the Juliascope transform (Transform 8), change the Weight from 3 to 4.

4. Adding a Final Transform

Step 1

To give our fractal more punch, we can add a final transform. The final transform will affect the entire fractal shape by influencing it with any formula or combination of formulas we choose.
Enable the final transform by clicking the Fx button with the little triangle at the top of the editor menu bar. You will see a grey triangle appear in the editor.

Step 2

This final transform begins just like any other new transform we add, with the linear variation set to 1. Remove this by switching to the variations tab and changing the value of Linear to 0.

Step 3

Add to the final transform 0.5 of the Foci variation and notice the change of the overall shape. Additionally, add in 0.1 Spherical. There is a slight, but visually appealing change to the shape of the fractal. Combining variations like this, even positive and negative amounts, can create some incredible images.

5. Cleanup and Rendering

The last few steps involve cleaning up the fractal and rendering.

Step 1

Close the editor and use the zoom and move tools in the main window to find a nice location on the fractal to render.

Step 2

Open the Adjustment panel and change to the Rendering tab. Change the Gamma setting to 3.5 for a slightly clearer render.

Step 3

The final step is to render the fractal. Open the Render dialog by clicking the purple gear in the main window. From here, set the Density to 10,000. The Filter Radius setting of 0.455 will work nicely for the detail in this fractal. An Oversample of 2 is ideal. Click Start to begin the render.

Explore the different final transforms first. Add several. Use negatives. Be bold! You will be amazed at the variety of images you can get just from changing these. Next, challenge yourself by removing the final transform and move some of the other transforms to new locations. Then, try changing the variations to create something new. If you would really like a challenge, start from scratch and try to create a hexagon or other type of tile.
Below are a few samples of what you can create with fractal tiles and Apophysis.

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