Informal Geometry

CONCEPTS OF FRACTAL GEOMETRY

The basic type of geometry which most of the us are familiar is the Euclid’s geometry. This type of geometry deals with the regular shapes such as the circle or the cube. If we dilate these shapes and examine any part of them, we will find that the shapes are smooth and that there are no irregularities. However, one does not always encounter the regular shapes in nature. For example, the fern leaf or a snowflake or the patterns on the seashells. Although these shapes cannot be classified as a part of Euclid’s geometry, they cannot be classified as chaos as well as this would not lead us to science. Therefore, this leads us to another type of geometry which lies in the middle ground. This is known as the fractal

But, this has a lot of deficiencies when it is applied to biological systems. Biological systems are mostly complex with irregularities existing to great extents. Development of tumours is one such phenomenon which deals with great levels of complexity. Since this formation is very complex its detection or diagnosis is also hugely complex. Histopathologists will recognise the similarity between periphery of a malignant tumour and the images of the Julia sets. Julia sets is an example of fractal geometry in which if we magnify any part of the shape, we will get the same shape once again. Similarly, in a tumour, from low to high magnification, the degree of complexity of the boundary remains relatively constant down to the level of the individual cells. Fractal geometry has a lot of uses like the one mentioned above in the modern everyday life. This article will focus on the application of fractal geometry in diagnosis of

Further, it should be kept in mind that many of the issues tend to common to the problems computer analysis faces. One of the main issues faced is the lack of standardization. When different algorithms are used to calculate the fractal dimension useful in the fractal analysis, there is a chance that one may get different result. Therefore, it is important that the researchers make a note of the methods used for the calculations. Moreover, the users of these methods may lack the technical expertise to understand the importance of these analysis tools to the input data. This may lead to significant variations in the