It has been known that nanoparticles, for example, exhibit quite different properties from the bulk samples of the same materials. Yet nobody knows why. We discovered a control method of the fractal dimensions of any solid sample, enabling systematic and detailed examination of various physical properties of samples with different dimensions. As a result we discovered the universal relationship between physical properties and fractal dimensions.
From heavenly bodies to human cells, everything in this universe? possesses finite dimensions in three directions in space, namely everything in the real world is three-dimensional, according to Euclidean geometry. However thin or small an object is fabricated by nanotechnology, the dimensions can not be altered. Accordingly, it has been firmly believed that nobody could change or control the dimensions of real matter. However, if we pay attention to fractal dimensions instead, dimension control is possible in a facile way.
We prepared a series of mixed powder samples with the same material but with different fractal dimensions, corresponding to a different mixed ratio between the substance of interest and wax. Using these samples, we examined their structures and various physical properties in detail. We also examined different materials with different properties to confirm the universality of the results. With the aid of theoretical calculation based on original models and methods, we discovered that there is a universal relationship between the sample fractal dimensions and their physical properties, such as electrical conduction and magnetism. This could be a newly unveiled principle of nature, where the dimension of matter governs all its physical and mechanical properties.