I had to go really old school, but I think I figured out how to do create this effect. I used Particle Playground, an effect that was created in 1992!
Drop your shape(I’m calling it the snowflake) into a new composition. Create a solid, add Particle Playground. PP has 3 different particle systems and you want to use the layer exploder system. So open up “Cannon” and turn the particles per second to 0.
Open up “Layer Exploder” and choose Snowflake. If you play right now, you will see two things. The particles falling off the screen and new particles being created. So first go to gravity and change Force to 0. Now, go to the first frame of your comp on the snowflake layer, set the an opacity keyframe at 100, move 1 frame forward and set the opacity to 0. Layer exploder creates particles where ever it finds some something in the Alpha/RGB channels. This stops the creation of new particles. In my example, in the Layer Exploder, I set the Radius to 5, you will want to adjust to taste. A radius one of one gives pretty cool results at the end, but will slow the render down.
Create a new composition and call it Repeller. This is where you will create your force. I started with a circle shape. Had a couple of keyframes move it across the screen, and added wiggle to it’s position. Next I created a solid, added turbulent noise and adjusted the settings to create an evolving noise map with a fairly high contrast. I used the shape layer as a luma matte for the noise. Finally, I added an adjustment layer and added colorama and set the output to RGB. Lastly, I added a fast box blur to make it a little bit smoother of a transition.
Add the comp Repeller to your main composition. Now just go into the Ephemeral Property Manager. The is the short term effects property, your map will affect the particles when it hits the particles but they go back to there initial state when unaffected. Set the Layer Map to your “Repeller” layer. Now twirl down the Affects and use one of the colors to map the X, One to Map the Y, and you still have a third that you can use to map any of those other properties. I chose scale. Adjust the Min/Max and Operators to taste and you are good to go.
Take a look at my attached example project.