How do I create more "blobby" Perlin Noise?

So normally perlin noise is a really smooth thing, but what I need is it to be mostly close to 0, but sometimes make blobs that skew out to high values.
Making the min. threshold big won’t help because then it mostly just spaws random dots. What I need is for it to mostly spawn nothing, but eventually spawn more or less big blobs.

Normal perlin noise:

What I need would kinda look like that:

You could raise the value to a power. The x values in the graph would be the perlin value you put in and the y the value you get out. Normally (or power of 1), the result would be linear, because x = y. By raising the value to a power, we can force the graph down towards 0. The powers are Green:1, Purple:2, Red:4, Blue: 8. With for instance a power 8, the resulting perlin field will stay close to 0 when its below 0.6 and only goes up after that value. In other words, the field will be flat and only if there is a significant peak it will create values.