Create a Hypocycloid Brush

With a somewhat tongue-twisting name, this hypocycloid is a pretty geometrical construction that slightly resembles a four-pointed star, but is more graceful with curves between the points instead of angles.




The Pittsburgh Steelers logo has three hypocycloids in it.


Not necessary, but nice to have is the guides-every-x-pixels script which is zipped and attached below. It saves a lot of time placing the multiple guidelines used in this tutorial. Unzip and save to your Gimp Scripts folder. Refresh the scripts in Gimp: Filters > Script-Fu > Refresh Scripts.

Open a new image, 600 x 600 pixels and fill it with white. Make a new transparent layer.

Image > Guides > New Guides Every X Pixels. Make the spacing 100 pixels. Then return to the same script and change Horizontal to Vertical and then OK. You will have guides going both directions on your image.

Select the Ellipse tool and make it a Fixed size, 200 x 200.



You will be making circles using the guides. The circles will automatically snap to the guides but be gentle as the snap isn't that strong. You can feel it snap. Make 4 circles like in the image below, by making the first circle and while holding down the Shift key, make the next 3 circles. Make them in the areas formed by the guides as pictured. When you are finished they will all be selections. You can let up on the Shift key.

Select > To Path.
Select > None

Go to Paths and you should see 4 circles in the path. Turn on the eye next to the path thumbnail. Return to the layers.


Next, use the Rectangle Select tool and make a square, Fixed, 200x200. Place the square in the center as shown below and fill the square with black.
Select none.



Select > From Path. The circles path is the activated selection. Press the Delete key. Your hypocycloid is finished.



Go to Image > Guides > Remove All Guides.
Go to Paths and turn off the eye next to the path thumbnail.
Go back to layers. Autocrop the hypocycloid layer. Right-click the layer and Flatten Image to the white layer.

Image > Mode > Grayscale.

Export the image to your brushes using a .gbr extension.

Flattening and making it grayscale will allow the brush to use the Foreground color. Also you can use brush dynamics.

Download a PDF document of this tutorial below.

Also attached is the zipped brush. Unzip and put into your Brushes folder.
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Very cool Oregonian

Nice!

Thanks O!

So how do you get the rainbow coloring like in the example?

Clearly written and the pointer to the guides every n pixel script is appreciated
Had not thought of doing this as a brush

2^nd 2-ton's request for info on the multicolor gradient example


any chance someone can generalize a tool to produce hypocycloids inside a user defined diameter with a variable number of cusps?

Wow, what a nice response. Thank you everyone. Love the helmet with the logo you made, Conbagui.

2-ton, that rainbow colored one was made using the Bevel Reflect Logo.

Make a new image, 300x300.
Use the brush you made, using the default size (180), foreground color black (000000).
Make one hypocycloid in the image with the brush, right-click the layer and choose Alpha to Selection.

Select > Shrink 2. Keep the selection.

Filters > Alpha to Logo > Bevel Reflect Logo.
Change the top choice - Bevel-Slope Options from Flat Bevel to Run Interactively. Click OK.
A second dialog will show up, you may have to get it from the task bar.

Click OK.
There will be 3 layers resulting. Right-click the bottom layer and choose Alpha to Selection.
Select > Invert.
Select the top layer and press Delete. Delete the invisible layers. Autocrop.

Thank you Oregonian for this make a brush tut and I like the guides script too!

excellent tutorial, Orergonian!
but because me (and maybe some other chatters -don't know) am lazy, could you post here the brush itself? maybe also others similar and creative as this one...thanks

There ya go, dinasset. Unzip and put into your brushes folder.

I've also attached it in the original tutorial post (first post in this subject).

Thank you Oregonian. I'll make your tutorial because I will learn new things to manage with Gimp.

thanks a lot, Orergonian, from the depth of my "lazy" heart!....


not a good use, only to say quickly my appreciation...

Thank you so much Oregonian. I followed your tutorial without any problem as you did it so clear.
Great script, too as the guides now are so easy to set.
Here my last outcome (my own brush is in my folder)
Nice decoration Dinasset,

Thanks OldManGrumpy, dinasset and Issabella. Love your results dino and Issabella!

I thought a bead curtain of them would be kind of cool.

Thanks O! It's so purdy!

You're welcome, 2-ton. Glad you like it.