Mathematics can help us draw real objects. The regularity of patterns in nature can guide artists to use mathematical concepts for artistic creation. Many plants have amazingly beautiful branches and leaves, in which we can find some mathematical models.

For example, aloe vera is a plant that grows in Lesotho (an African country). They have beautiful spiral leaves.

There are many ways to construct the shape of leaves with mathematical concepts. A famous example is the ferns in barnsley. Michael Barnsley, a famous British mathematician born in 1946, described this beautiful fractal structure in his book Fractal Everywhere.

He created this fractal by the method of iterative function system, which is very similar to the leaf shape of ferns.

When I want to draw a physical object, I will try to find a mathematical formula to draw it step by step. At every step, I will add mathematical expressions to the function to enhance the similarity between painting and objects.

Generally speaking, I always look for formulas about sine and cosine, because their characteristics (especially periodicity, boundedness and smoothness) make them very useful in painting.

But I still have to find a suitable mathematical expression in each step, so some steps will be difficult or even impossible to complete.

For example, in the picture above, you can see the generation process of a mathematical curve similar to the shape of a Japanese maple leaf. The image shows how to turn a circle into a maple leaf.