As a tree grows, it sends out boughs, branches and smaller growth that diminish in width as they grow. Therefore, when you sketch a bough coming from a trunk, remember not to make it the same thickness as the trunk. The same principle applies to branches from boughs and to smaller growth, like twigs, from branches.
In the bottom drawing, you see a branch that appears to grow from the tree toward you. This is called foreshortening. You can create the illusion of foreshortening by making the branch larger as it comes toward you, and smaller at its place of origin. You can carry this illusion further by including more detail in the branch the closer it gets to the viewer's eye. Another way to give the appearance of foreshortening is by darkening the trunk behind the branch and lightening the branch coming toward you.
Often a growth from the tree will leave an indentation in the main trunk or grow a sort of collar around the circumference. Including this in your drawing gives the boughs and branches a look of being attached or belonging to the trunk. And be aware that when branches grow downward, they should be drawn lighter in value, since they get more light. When they grow upward, they should be darker in value. Drawing the upper sides of branches in lighter values and the lower sides in darker values gives the appearance of roundness and weight.
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