This paper discusses the effects of applying different non-linear transformations in combination to well-known fractal structures and aggregates, to obtain novel fractal images. Five different non-linear transformations are selected to be combined, and applied to existing aggregates, and the new fractal structures obtained are discussed. We show how different non-linear transformations effects (bending effects, diffusion effects, etc.) can be combined just by function composition processes, and their final results as new fractal images. We analyze the effects of the combination of non-linear transformations over classical fractals such as the Sierpinski triangle and Sierpinski carpet, in terms of the fractal dimension of the new structures created. Finally, we will also show the effect of the non-linear transformation on other fractal structures, such as diffusion limited aggregation and strange attractors.