Download INKPAD by TAPTRIX INC from the App Store. (Free)
There are five parts to this Wallpaper, the background, the circles (big,medium,small), and the curves.
This is how it looks on the lock screen.
And this is how it looks on the home screen.
Go to Apple's website to find the dimensions of your device. I have an iPad mini so my dimensions are 1024x768.
Open Inkpad and tap the white plus at the top right of the screen.
A window pops up. Tap the blue arrow next to "Custom size."
Type in the dimensions you found on Apple's website and make sure "pixels" is selected. Were says "New drawing." (1024 x 1024 actually works better but for the guide I used 1024 x 768).
Then tap "create" to create a new drawing.
Tap "Layers" at the bottom right of the screen.
Tap the white plus to create two new layers.
Tapping the name of the layer allows you to change the name of the layer. Make a layer named "Curves, a layer named "Circles," and a layer named "Background." Select the background layer.
Select the "Square tool." Select a color for your square. I chose a very light grey.
Drag out a square over the entire canvas.
Choose the circles layer and tap the "Circle tool."
Drag out three circles, one big, one small, and one medium sized. The gear at the top right of the screen is where you can turn on snapping to make sure the circles stay circular.
You can take away the white stoke around the circles also. By choosing "None" under the stroke menu. Choose a color for these circles under the "Fill menu."
Select the circles with the selection tool (looks like an arrow).
Tap "Edit" and then tap "Duplicate."
With the duplicates still selected, tap the "Rotate tool," and swipe your finger over the canvas in a circular motion.
Change the color of these circles
Do the same for other groups of circles.
Now for the curves. Choose the curves layer. You can lock other layers by tapping the padlocks next to them, this will prevent you from accidentally modifying other layers.
Choose the "Pen tool" and take away the fill by choosing "None."
Give it a white stroke.
With the pen tool selected, tap on the canvas once, and then tap a second time in a different location. This creates two connected lines. You could make as many likes as you would like.
With the selection tool selected, double tap on a point on the lines to make a curve at that point.
Moving the blue handles adjust the direction of the curve.
With the curve selected, choose the "Rotate tool." A little crosshairs will show up on the canvas.
Tap at the first point of the curve to place the crosshairs there. This crosshairs is called a "Pivot." Your curve will rotate around the pivot.
Now duplicate the curve as we did with the circles using "Duplicate in place." Then drag in a circular motion to rotate the duplicated curve.
Do it as many times as you would like. I also made my stroke a little thinner.
Done! Tap the "Send arrow" at the top right of the screen.
Tap "Add to photo album."
This is the final image.
Go to you photos app and to your saved photo. Tap the blue send icon at the bottom left of the screen.
Choose "Use as wallpaper" at the bottom.
I set my wallpaper to be used on "Both" the lock and home screens.
Examples: (tap and hold the image to save it)