Logos, Line Art, and Vector Graphics

Pixlr is a great free image editor for patterns & https://vectr.com/ is good for vector graphics and line art (such as logos).

Vectr is a free graphics software used to create vector graphics. You can download this app for free, or use it through your browser. Pixlr is a little more intuitive than Vectr, but both are awesome free programs usable online.

Related Question:
Saving an image as a Bitmap (using Pixlr)