I am aware of this question, however it appears to be for Blender Internal exclusively. Is there a way to do this in Cycles (Blender 2.7+)? And would an animated texture work as well?
2 Answers
It works the same way for cycles. Also if you have an animated texture (image sequence or procedural) the animation will effect the length as well.
- In the Textures section of the Particle settings for your Particle system, add a new texture.

- Now in the Texture tab, change the Influence to Length.

This animation was made by animating the Size on the Distorted Noise texture that is controlling the length of the particles.

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Weight Paint offers an alternative to using textures and works nicely with Dynamic Paint. Vertex Weights for various particle attributes can be selected in the Particles settings tab.

Add a vertex group to the ground plane which has the particle system and make the ground plane a dynamic paint canvas. For this simple example, I left the vertex weight group name as the default name "Group".
Make the sphere a dynamic paint brush.
The settings are mostly default except for what I've circled in the image. You mostly just have to assign the vertex group to both the sphere and the ground and change the paint type to Weight
The grass is a simple object named Plane.001, the name is shown in the particles tab as the render object(the object is not shown here, it's on Layer #2).
(i)The ground 'canvas' settings

(ii) The ground particle settings

(iii) The sphere 'brush' settings.

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