From number theory to knots, Hecke algebras have applications within many areas of mathematics. In this talk we describe a pictorial calculus for computing convolution products in affine Hecke algebras over fields of characteristic zero. Convolution products of this type have been understood since the work of Iwahori and Matsumoto [1965]. However, using results of Parkinson, Ram and Schwer [2006], we can now draw pictures illustrating the rich combinatorial nature of these products. We describe this pictorial calculus in the example of $\mathrm{SL}_3(\mathbb{Q}_p)$. Its applicability is limited to characteristic zero.