Multiple-point simulation is a family of methods used to generate conditional facies simulations that present the same spatial dependence as a user-defined training image. The main advantage of using a training image is the easy integration of geological concepts in numerical subsurface models. The strength of multiple-point methods is that it allows making the best use of geological expertise when data are too sparse for inferring a model of spatial continuity. However, despite being appealing to geologists, the multiple-point methods are often not used in practice due to the difficulty of building complex 3D training images that contain realistic features.A new framework for multiple-point simulation is presented that involves small and simple training images. The main idea is to use random transformations to expand the range of structures available in the simple training image. The training image is not regarded any more as a global conceptual geological model, but rather a basic structural element of the subsurface. Complex geological structures are obtained, whose spatial structure can be parameterised by adjusting the statistics of the random transformations, based on field data or geological context. In most cases, such parameterisation is possible by adjusting two numbers only. One advantage is that the training images are so simple that they can be easily built even in 3D. The method allows building 3D models that reproduce shapes corresponding to a desired prior geological concept and are in phase with different types of field observations, such as orientation, facies or geophysical measurements. The flexibility of the approach allows for naturally integrating different types of data. This is demonstrated on an example involving seismic data assimilation. Examples where complex 3D folded structures are built from a simple training image and a few orientation data are shown.