Where do the most popular online cultural artifacts such as image memes originate? Media narratives suggest that cultural innovations often originate in peripheral communities and then diffuse to the mainstream core; behavioral science suggests that intermediate network positions that bridge between the periphery and the core are especially likely to originate many influential cultural innovations. Research has yet to fully adjudicate between these predictions because prior work focuses on individual platforms such as Twitter; however, any single platform is only a small, incomplete part of the larger online cultural ecosystem. In this paper, we perform the first analysis of the origins and diffusion of image memes at web scale, via a one-month crawl of all indexible online communities that principally share meme images with English text overlays. Our results suggest that communities at the core of the network originate the most highly diffused image memes: the top 10% of communities by network centrality originate the memes that generate 62% of the image meme diffusion events on the web. A zero-inflated negative binomial regression confirms that memes from core communities are more likely to diffuse than those from peripheral communities even when controlling for community size and activity level. However, a replication analysis that follows the traditional approach of testing the same question only within a single large community, Reddit, finds the regression coefficients reversed -- underscoring the importance of engaging in web-scale, cross-community analyses. The ecosystem-level viewpoint of this work positions the web as a highly centralized generator of cultural artifacts such as image memes.