“I improvised on a recipe that I found in a magazine.”

You made a dish to bring to a potluck, and someone commented on how good it was. She asked where you got the recipe. You used a recipe from a magazine, but you made a lot of your own changes to it, so you say:

I just improvised on a recipe that I found in a magazine.

improvise on (something)

The word "improvise" is closely tied to jazz music. Jazz musicians don't learn the exact notes to a song. Instead, they learn the general outline of a song and then make up parts of the music as they're playing.

People use the word "improvise" in a similar way to talk about doing things without a plan. For example, you can "improvise" for a presentation:

I couldn't open my PowerPoint presentation, so I just had to improvise.

To "improvise on" something means to start with a plan, structure, or recipe that's already been made, and then add things to it.

a recipe

A "recipe" is a set of instructions that tells you how to make a certain kind of food.The recipe lists the ingredients that you need, then tells you how to cut, combine, and cook it all.

On packaged food, sometimes there are instructions printed on the side of the box or bag. We don't call this a "recipe". We call it "instructions":

I just followed the instructions on the box.

When you want to talk about the food that you made with a recipe, there are different words for different kinds of food: "a dish", "a salad", "a pie", etc.:

Paula brought this amazing dish to the potluck. It was so good!