background_test.py

from kivy.app import App
from kivy.lang import Builder
from kivy.uix.widget import Widget
from kivy.core.image import Image
from kivy.properties import ObjectProperty

Builder.load_string("""

<BackgroundTest>:
    canvas:
        Rectangle:
            pos: self.pos
            size: self.size
            texture: self.texture

""")

class BackgroundTest(Widget):

    texture = ObjectProperty(None, allownone=True) 

    def __init__(self, **kwargs):
        super(BackgroundTest, self).__init__(**kwargs)
        self.texture = Image('pattern.jpg').texture
        self.texture.wrap = 'repeat'
        self.texture.uvsize = (3, 3)

class BackgroundTestApp(App):

    def build(self):
        return BackgroundTest()


if __name__ == '__main__':
    BackgroundTestApp().run()

pattern.jpg

Initially, everything looks good:

But as soon as I resize the window, the background breaks: