There is no one way to answer this question. There are many in which art and science are related. Let me name a few of them.
First, often times art is beautiful due to proportions. If this is so, then we can say that science and math are related in important ways. The same can be stated when it comes to art that is based on geometric patterns.
Second, art is also very analytical. Some of the greatest artists in the history of the world were also very analytical scientists. This point might seem amazing, but think of people like Michelangelo. He was an amazing artist, but he also possessed an amazing scientific mind.
Third, when we think of science often we do not think of creativity, but some of the best science today is based on creativity. From this perspective, we can say that the arts are clearly related.
Loosely speaking, in science you conduct experiments to get results and in art you simply 'experiment' with different mediums to get the desired result as well.
- Research: You have to understand what you're doing and what you're using. If you don't know the basics, it will be considered a recipe for disaster.
- Problem: What's the problem or challenges to this experiment that you'll be performing?
- Hypothesis: How will you go about challenging the problem and hoping for success?
- Experiment: The actually trial and error experiment.
- Results: What have you analyzed throughout this entire process?
- Conclusion: What have you learned from the experiment you've conducted? What can you do better?
Although these would be considered guidelines to conduct a scientific experiment, these guidelines can incorporate exploration through art.
Probably the most popular use of art in science is with emotions in the brain. Many use music as an expression of their feelings. Many will use music as an outreatch to try to feel better (such as listening to Adele "Someone Like You" when someone breaks up with you). Another way that is similar is the playing of a musical instrument. Many (including myself) play an instrument and use it to express themselves. They will play sad songs when they're sad, happy songs when they're happy, ect.There also is such a thing as musical therapy.
Hope that helps