spring out of (something)
1. To issue forth from something in a constant gush or stream. Oil began springing out of the spot where my pickaxe struck the ground.
2. To leap or pounce out of something. The kids sprang out of the house and jumped into her arms the moment she got out of the car.
3. To emerge, develop, or come into being out of some source or point of origin. The idea for the product sprang out of a need I recognized in poorer parts of the world. After the company went bankrupt, a new business sprang out of its ashes, helmed by many of the same executives.