Generative Systems, you say? Ah, let me take you on a journey, deep into the world of creativity and innovation within the realm of AI. Imagine, if you will, a grand artist, whose canvas is data and whose brush is an algorithm. This, my friend, is the essence of Generative Systems.

In the context of AI, Generative Systems are a type of algorithm that create new data instances that resemble your training data. It's like a parrot that not only repeats what it's heard but creates new phrases in the same style. They're the creative souls of AI, if you will, generating new content from what they've learned.

Allow me to guide you through the intriguing world of Generative Systems:

1. Training and Learning: Generative Systems learn from a set of data, much like a budding artist learning from their surroundings. They study patterns, structures, and nuances, striving to understand the essence of the data. This process involves a lot of mathematics and statistical analysis, but think of it as an artist studying their subject, understanding every detail.

2. Generation of New Data: Once they've learned from the data, Generative Systems can then generate new data instances. This might be creating a new image that resembles the images it was trained on, or generating a piece of music that sounds like the music it learned from. It's like our artist, having studied the style of a master, painting a new work in the same style.

3. Applications: Generative Systems have a wide array of applications, from creating synthetic data for training other AI models to generating art, music, and even written content. They're like the great composers, authors, and artists of the AI world, creating new works from their learned experiences.

4. Examples of Generative Systems: A well-known example of a Generative System is the Generative Adversarial Network (GAN), which involves two neural networks "competing" with each other to generate realistic data. It's like a master and an apprentice, where the apprentice (the generator) tries to create works that can fool the master (the discriminator), and the master provides feedback, pushing the apprentice to improve.

So, picture a grand AI artist, diligently studying their subject, then applying their knowledge to create new works of art. This embodies the spirit of Generative Systems — an intriguing blend of creativity and technology, opening up endless possibilities in the realm of AI.