Inkscape

A free software for editing vector files. One of the free alternatives to Adobe Illustrator.

How to turn an image to a symbol

Import the image into the canvas. We will use the image to trace the lines on it. As a personal preference, reduce the opacity of the image to make it easier to see your work in progress.

Then it's all free from here. For a start, you can use the calligraphy and the bezier curve tool.

Repeating patterns on a shape or path