I really enjoy these images, I know the second one is from a game, I'm just hoping someone can tell me what these types of art might be categorized as so I could get more into them. Thanks.
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The second image is from the game Firewatch, which was visually developed by artist Olly Moss, of Mondo poster fame. http://ollymoss.com/
This is a form of minimalism. It's marked by strong, geometric shapes and pared-down design elements. Often, a single dominant image stands alone to deliver a powerful message.
In Moss' work, bold, layered colors create a sense of depth and distance. The farther in the distance objects are, the more they fade into simple colors and fewer details.
Another classic example of this style is work by the designer Saul Bass.
A traditional method which shares features of those images is wood block printing.
Obviously, this is a method rather than a style, but considering the large block forms of single colors, this method is probably the closest.
Serigraphs (silk screen) share some features but they are more easily able to use gradients and shading.