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You can use a texture to drive the "Push" deformer:
1. Select your object.
2. Property / TextureMap / TextureMap and select what mapping method you like. Select a black and white image. Rename the texture map property to something you can easily remember like "Test_Texture".
3. Select: Deform / Push
4. Select the "plug" icon next the Amplitude slider and choose connect.
5. You should see your texture map on the object's list. Select "Test_Texture" or whatever you called it.
6. Now when you slide the amplitude you should see the texture map displace the goemetry.
7. Freeze the object when you are done to make the deform permanent.
Note: Be sure the goemtry has plenty of polygons to handle the detail. Blur edges of the texture to smooth edges of the deform.
Hope this helps,
Ohmanoggin