While we cannot plot the complete shape of the futures curve, chartists can plot the difference between near-term futures prices and forward futures prices to find out if market structure is in contango or backwardation. This is important to markets like oil because market structure reflects current and future demand prospects.
In general, market structure is contango when near-term futures prices are lower than the more distant futures prices. For example, contango would be present if May Light Crude (^CLK15) was priced below October Light Crude (^CLK15). Backwardation is the opposite and occurs when near-term futures prices are higher than more distant futures prices. Backwardation would be present if May Light Crude was priced higher than October Light Crude.
The chart above shows May 2015 Light Crude (^CLK15) in black and October 2015 Light Crude (^CLV15) in red. I am using the "price (same scale)" overlay to plot them together (see image below). The middle window shows the difference between October Light Crude and May Light Crude. Market structure is contango when October Light Crude is price higher than May Light Crude. Backwardation is present when October Light Crude is priced lower than May light crude. Note that I selected price as an indicator and entered ^CLV15-CLK15 in the parameters box to create this plot. Also note that chartists can search the terms "oil and cme and 2015" to find all our symbols for crude oil futures.