Quick Maps
Quick Maps are a fast and fun way to change the particle grid. They can, for example, be used to map a color gradient over X, Y, or Z axes; change the size of the particles over an axis; or even change things like dispersion and fractal strength. Quick Maps are convenient because they are generated within Trapcode Form and need not be created ahead of time on a separate After Effects layer. Note that Quick Maps are always applied to the grid first, before any displacement fields are applied to the form.
Types of Maps: Values and Colors
There are two types of map controls, one that defines arbitrary values for a control and axis and a color map for creating color gradients that can be applied across the form. Note that the Opacity and Color Maps are linked together.
The Value Map
Value maps are available for Opacity, and for the three arbitrary maps #1-#3. These maps offer 3 custom controls: the drawing area, the presets, and the commands. The drawing area lets you add a freeform value by painting values across the area: values near the top represent a maximum, and values near the bottom represent a minimum. Here is the curve-drawing interface to set the map's values:
To draw a curve, click and paint inside the drawing area. When your mouse enters the drawing area, it will change to a cross-hair. As you click in the area, the value is redrawn between the bottom and top of the area. The smooth curve above would be drawn by dragging the cursor near the bottom on the left, holding the mouse down and sweeping toward the top, then moving to the other side of the graph and sweeping from top to bottom on the right. Strong smoothing was then applied by shift-clicking the Smooth command button.
Select a preset
To select a preset, click it. The curve presets offer 6 preset value graphs arranged from top to bottom. Clicking one sets the control area and cannot be undone. From top to bottom, the presets are: full on, linear decrease, linear up and down with a peak around 25%, fade on and off, part on / part off with a smooth transition, and part on / part off with random noise.
Commands
Smooth - makes the curve smoother. Hold down Shift for extra strong smoothing.
Random - completely randomizes the curve.
Flip - flips the curve horizontally.
Copy - copy this curve into clipboard. Once Copy is clicked, a Paste button is enabled in the other map areas.
Paste - paste curve from clipboard.
Color Map
To set particle color over a chosen axis, Trapcode Form offers a gradient design interface:
The color gradient consists of a number of color boxes. The gradient is interpolated between the boxes.
The Opacity and Result bars are here to give an idea of what the resulting color gradient will look like, once the alpha from Opacity from the Opacity value map is applied.

A base grid without Quick Map | Grid with Map+Opac over X

Add a color box
To add a color box, click in the area just below the gradient (dotted in the image above). The box will initially get the color the gradient has at that position.
Change the color of a gradient box
To change the color of a box, double-click it and the system color picker will come up.
Move a gradient box
To move a box, click and drag it sideways.
Delete a gradient box
To delete a box, click and drag it downwards.
Select a gradient preset
Trapcode Form includes some popular gradient presets. To select one of the presets, click it.
Commands
Random - all boxes' colors are randomized.
Flip - all color boxes are flipped around the center.
Copy - copy this gradient to clipboard.
Paste - paste gradient from clipboard.
Quick Map Control Areas
Opacity Map
Defines the alpha channel for the Opac+Color (the opacity plus color) map where the Y axis of the graph defines the maximum value and the X axis of the graph defines the location of the chosen axis of the grid (X, Y, Z, or Radial).
Color Map
Defines the RGB color values for the Opac+Color map across the specified axis.
Map Opac+Color over
Defines in what direction to map. You can choose from Off, X, Y, Z and Radial settings. The map appearance will change based on the size, and particles in X, Y, Z as set in the base form area. The example below shows a default Opacity map where the values are unchanged and the default rainbow color map has been applied.

Off | X | Y | Radial

Map #1 - 3
These maps can be assigned to a range of parameters: Size, Opacity, Fractal Strength, Disperse and the Audio Reactors. Here are several examples (all mapped over X) using the following value graph:

Off | Opacity | Fractal Strength | Disperse

Advanced Example
Here is a more advanced example where we take a base grid:
Then we apply the following settings to the map. The opacity and color create a green area that is opaque only in the center of the X axis. The Map #1 graph defines the particle Size along the Y axis, causing the size of the particles to decrease and then disappear toward the bottom of the screen. Finally, the Fractal Strength field is modulated across the X axis with Map #2, so it only affects the center of the grid (note that Fractal Field Displace is set to 12):
The result is this animation: