Greetings to aspiring data scientists! Today, we'll unlock the curious world of the DBSCAN (Density-Based Spatial Clustering of Applications with Noise) algorithm. Standing out in the clustering landscape, DBSCAN is famous for its resilience to outliers and for eliminating the need for pre-set cluster numbers. This lesson will demystify DBSCAN through a Python-based implementation from scratch.

Let's start by peeling off the layers of DBSCAN. At its core, DBSCAN operates on concepts of density and noise. It identifies clusters as regions of high density separated by lower-density regions. Concurrently, it classifies low-density entities as noise, enhancing its robustness towards outliers. The secret recipe behind DBSCAN? A pair of parameters: Epsilon (Eps) and Minimum Points (MinPts), which guide the classification of points into categories of 'core', 'border', or 'outlier'.

With a foundational understanding, it's time to roll up our sleeves and implement DBSCAN from scratch.

We'll create a simple toy dataset using numpy arrays for the first hands-on task. This dataset represents a collection of points on a map that we'll be clustering.

Next, we'll devise a function to calculate the Euclidean distance between the data points. The function uses numpy's linalg.norm to evaluate this distance, which reflects the shortest possible distance between two points.