To follow a single ink molecule, one first solves the classical diffusion equation (with Subscript being the diffusion coefficient)Īnd then follows that path , In our case, the initial letters have a lot of ink and the space between the letters is ink-free. If one imagines a liquid with time-and position-dependent concentrations n(t,x,y) of say ink, the ink will spread to a uniform distribution in the long time limit. (Because we don't want to preserve the character weights/areas, we will use different boundary conditions.) The use of the diffusion equation to spread out areas was pioneered by Gastner and Newman in building cartograms in their cartogram algorithm. follow the boundaries of the letters under this diffusion process.Of the words diffuse/flow into the space between the words/charactersĪnd between the characters and the boundary of the outer shape solve the diffusion equation (using NDSolve) to let the characters.make an initial word cloud (using WordCloud) within a given shape.Our overall approach will be the following: To keep this post at reasonable length, let's try to reproduce the first two features: a dense packing of characters that fills a given outer shape. the Illini coloring is correlated to the flow of the robe.the characters of a given word are not all the same size, but the.The character is still recognizable (like in a CAPTCHA) the characters fill out most of the space with smooth outlines, but.

the words are all contained in the outline of the Alma Mater.

This hand-made poster has many nice elements, e.g.: That is an interesting problemhow to make such-type deformed dense letter arrangements in the Wolfram Language.

With only a few weeks until this year's marathon left, I will give this a try. While doing so, she asked me if it is possible to make artistic word clouds, such as the one from the 2017 Champaign-Urbana marathon poster (that hangs on her office door) using the Wolfram Language. Some time ago, my coworker Eila Stiegler was working on her blog about the cool Marathon visualization website. Finance, Statistics & Business Analysis.Wolfram Knowledgebase Curated computable knowledge powering Wolfram|Alpha. Wolfram Universal Deployment System Instant deployment across cloud, desktop, mobile, and more. Wolfram Data Framework Semantic framework for real-world data.

Word cloud mathematica