ONe of my favorite characters in Shakespeare, Ariel.
Your landscapes from the air, are they moving or are they stills?
How do you want the final image to build? Do you want to see the individual brushstrokes applied? Or is this a slow dissolve from initial state to the end state? Is the motivation for the effect legitimized in the storyline or is it gratuitous?
The answers will help us suggest which set of third party filters you start saving for.
Chris presents a stylized transition that moves from one image to another, not necessarily a transition from a plain image to stylized version of the same image. If you download and open the 2013 version of his project, you will see he accomplished his transition with just the basic AE tools but he applied them iteratively to 25 precomps that open up into more than 100 layers.
The stylization of an image into a painting can be done easily in Photoshop. To animate it in AE takes a special third party filter like, say, VanGhohist from DigiEffects BErserk (now obsolete), or, as Zwar has demonstrated, a solid foundation in many basic tools like vector blurs and displacement and compound effects that accept input from an unseen layer and use it to modulate another layer. Emboss, Color emboss, Colorama, Brushstroke, Glass, Edges, Displacement, Scatter, Ball Action. You could create a drive layer from Fractal Noise and uise that, over and over, to create displacement and blur and then use edge detection or embossers to simulate texture in the paint or paper or canvas. It's a long list. It's a long process. It's a blast.