Welcome to Queen's Landing "Figure 1" showcases Queen's Landing, a 3D visualization of the 8-Queens problem that I've been diving into from a fresh perspective. After unpacking the problem in my recent posts, a brainstorming session with a friend sparked this cool concept: visualizing the energy (think synapses) of the neural network I've engineered for this puzzle. The results? Absolutely breathtaking. By adding a visual dimension to the neural network's energy, we unveil not just striking concept art; we uncover patterns or nuances previously overlooked. Wikipedia might tell you that solving the Queens puzzle is daunting, with 27 being the largest board size humanity has unraveled. But what if we could distill the essence of the problem, visualizing solutions on a chart? That's the real teaser. But before we get into that - how does this levitating purple island, echoing a Spyro vibe, connect to an obstinate ancient math puzzle? Did you notice the dots? Each represents a chessboard configuration with 8 queens. These dots aren't placed haphazardly - the lower ones, tinted red, sit low, symbolizing viable solutions (check out my chessboard snapshot in the top right). Conversely, the higher, brighter dots indicate trouble spots - scenarios where queens are set to clash (imagine placing them diagonally). If you've been following my queen series, you'll see where this is headed: the dot's elevation signifies the network's energy level, with zero energy marking the bullseye, and high energy indicating a miss. The z-axis? It illustrates the energy for a given (x,y) board configuration. How do (x,y) dimensions map a chessboard, you wonder? By my calculations, a chessboard is more than a 2D entity. If AI isn't your thing, think of it as squinting to compress a 3D space into 2D, albeit with a few extra dimensions thrown in. What emerges are chessboards that compose this fantastical island. Really - the island is a mosaic of boards, look closely and you'll spot them. For the tech-savvy, that's t-SNE enhanced with a touch of interpolation magic. Dive deeper into the realm of floating islands in our project hub -> dorpascal.com/hopfield-network-simulator #open_to_work #cs #bsc #c #cpp #python Published on LinkedIn on April 6, 2024