Alkyl Shifts

[1,3]-Alkyl Shift

Figure 1:) [1,3]-Alkyl Shift 

     In figure 1 above, the alkyl R group is migrating from carbon 1 to carbon 3 via a 4π system.  The electrons bonding the R group to the carbon transition from C1 and bind to C3, bringing the R group along with it, while pushing the electrons in the double bond to C1 and C2 to fill the carbocation left behind by the transitioning R group.

[3,3]-Alkyl Shift 

Figure 2:) [3,3]-Alkyl Shift

In figure 2, a 6π rearrangement occurs where the pi electrons cycle counterclockwise to the adjacent carbons to yield the product. The reactant's C1-C2 double bond pi electrons move counterclockwise one carbon to become the product's C1-C2 double bond. This happens with the C3-C4 single bond electrons, breaking to become C5-C6 double bond in the product.  Likewise with the C4-C5 pi electrons forming a single bond in the product as the C3-C4.