Mandalas, Networks, and Graph Theory

So I was thinking about the Kahn-Kalai/Erdos Sunflower Conjecture, Euler, graph theory, quaternions, Appolonian gaskets and other mathematical objects… I needed a way to relax, and decided to make hundreds of these mandalas (or yantras, if strictly geometrical). The origins of mandalas may be prehistoric as well as pancultural. Traditionally representing the cosmos, the construction of mandalas signify balance and their destruction marks a transformation. Mandala is from the Sanskrit for “circle”, and is also a unit of 48 days in the yogic system. By the way, mandala networks are also a thing! I think *eventually* I’m going to write about these connections, but in the meantime, here are almost 200 free mandalas for your viewing or coloring pleasure… I recommend inverting the image and coloring in neon, but that’s just me

Click here for mandalas!

Below are some of the most recent interesting finds I’ve encountered in my studies of mandalas.

Mandala Networks

“…here we will address the challenge of providing a paradigm for complex networks with better topology. More precisely, we show that it is possible to design a family of scale-free networks which are robust to random failures and considering some modifications, we can improve the resilience against malicious attacks. Additionally, these networks also exhibit other improved properties, like a finite shortest path and extreme sparseness in the thermodynamic limit, which substantially increases communication and reduces costs. Thus these new networks become potential candidates for the design and implementation of complex infrastructural networks.”

https://www.nature.com/articles/srep09082

Expressing the Elements of Failure through Mandalas

“If we represent the same information as a cladogram, we have a structure such as in Fig. 4, Caption (b). If we then collect all of the “parents” (along with their “children”) that are identified as causes of failure and combine them in a single diagram, with lines drawn to show links as in a node diagram, we have a structure such as in Fig. 4, Caption (c). This type of diagram maps all of the elements of cause of failure and illustrates their hierarchical relationship.”

http://www.shippai.org/fkd/en/infen/mandara.html