So I want to use a png as the background for my android application.

The condition is that the biggest snowflake:

is always at the top right corner. I can scale the image proportionately only, because otherwise, the snowflake will end up looking like a bunch of I don’t know whats:

Given the plethora of device resolution and dpi’s available, what is a reasonable way to achieve what I want?
Update:
I am aware of 9-patch. But my background cannot be expressed in terms of a 9-patch. At best, what I can do is include the source in the largest dimensions (proportionately) possible. In my case, the source is 1920X2400 in size. To rephrase my question, what would be the safest size (with uniform scaling) to include in my app?
Here’s an example:

Image copyright of original authors. Used here, only for illustration.
I would do it like this:
Use
RelativeLayoutto set the image at top right corner of its parent container, and resize the image proportionally according to the screen sizeexample:
As long as you provide the image via
android:srcandroid automatically resizes it preserving the ratio.