Eating Habits and Brain Function, are they related?

I had a question that I can't stop thinking about..

Are the vegans (and the malnourished) incapable of thinking as much as people who have a better diet?

I am personally an omnivore. I KNOW that the brain uses about 20% of our daily caloric intake for functioning. If I eat the base/minimum for my BMI, about 1,500 calories just to be a vegetable and lay down all day, I will not be able to think a lot, or do difficult things. If I get my work out and eat some 3,000 calories, I can actually use the work out/pump to flush my brain with oxygenated blood and lots of nutrients, and bio hack myself to rapidly learn skills.

I started meeting a new crowd of people, and I realized an "invisible" divide: diet and the ability to use the brain.

There's a clear disparity between people who are strict vegans, and everyone else, who might just be vegetarian but eat enough. It reminds me of one of my friends, and my ex wife, who battled teenage ED's but recovered (in the case of my ex) and gained healthy weight back/brain functioning.