Color palettes with more colors will make it easier to detect small variations. Try Red-Green-Gold Diverging, Sunrise-Sunset Diverging, or Temperature Diverging
If the viewer needs to see variation between similar values but most values have a nearly identical color then filtering out outliers will increase the color range available for the similar values. See Filter Data from Your Views
In order to select or choose palette without gray or white in the center please follow the steps
Click on the field you want to color (like a dimension or measure).
Drag it to the Color shelf (in the Marks card).
Click on the Color legend → Edit Colors.
Tableau will show you default palettes (like "Tableau 10", "Color Blind", "Gray", "Traffic Light," etc.).
From the Palette dropdown, choose the palette you like.
Click Assign Palette → then OK.
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