You can bake your material to an image. "Render" tab, at the bottom.
Edit: request for more datials on baking process. I assume you are using Cycles as render engine First you need to UV-unwrap your object
- Select your object (the sphere)
- Go to edit mode
- Select the equator edges of the sphere and make them a seam for UV unwrapping
- Select all faces ("a") in edit mode
- Open UV/Image editor in addition to 3D editor window
- Add a new image to UV/Image editor of desired size e.g. 1024x2024. The empty image should be double as wide as it is high, as you will have to place to circular meshes from UV unwrapping on the image.
- With all faces selected, click on UV unwrap in the mesh menu of the 3D editor window --> as a result, two circular meshes should appear in the UV/Image editor.
- Place the two meshes side by side on the area of the new image
- Select you material in the material tab
- Open a node editor window and add a new Image texture node. Do not link the new node to anything, but leave it highlighted.
- In the Image texture node select your newly created image as linked image
- now find on the Render tab the "Bake" submenu.
- select your baking method (combined should be ok) and check the options to your needs
- Click on the "Bake" button.
Now Blender should start to render the unwrapped sphere to the new image. The image can be saved and edited in an image editor.