1. **Inkscape**: Inkscape is a free and open-source vector graphics editor that can be used for creating and manipulating multi-layered designs. It supports up to 999 layers, making it suitable for your requirement.
2. **GIMP (GNU Image Manipulation Program)**: GIMP is a free and open-source image editing software that can handle multi-layered images. It supports up to 256 layers, which should be sufficient for your needs.
3. **Krita**: Krita is a free and open-source digital painting and illustration software that offers a powerful layering system. It supports up to 100 layers, which is more than enough for your simulation.
4. **Paint.NET**: Paint.NET is a free image and photo editing software that provides a user-friendly interface and supports multiple layers. It can handle up to 99 layers in a single image.
5. **Photoshop (trial version)**: While Photoshop is a paid software, it does offer a free trial version that you can use to test its layering capabilities. The trial version supports up to 999 layers, which should meet your requirements.
6. **Affinity Photo**: Affinity Photo is a professional-grade image editing software that offers a free trial version. It supports up to 16,777,216 layers, far exceeding your need for 15 layers.