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I'm looking for a library that I can use to display graphs with hours on one axis and days on another axis, where the cells are colored based on their value. Here is a draft of what I mean: 
Ideally the chart would auto-scale as data for more days are added, and the resolution of the y axis should ideally be adjustable. It's OK if the chart of the library has inversed axises.
Does anyone know about such a library? Or, do you know if there is a term for such charts?
Essential Schedule for JavaScript is a JS based library to consider.
The whole suite of controls is available for free through the community license program if you qualify. Note: I work for Syncfusion.
I fail to see your problem. Any charting library can do that; try D3Js or ChartJs, for instance.
You just have to provide data and labels. In the case of your blue boxes, every charting library I have tried allows you do define a callback function to determine cell content of even CSS styling. That's a single if/else statement.
I really fear that I have misunderstood your problem, as I see no problem. Perhaps you could elaborate? As it stands, it seems to trivial that I agree with @Binvention's comment that you could easily code it yourself.
