The use of drones in filmmaking

Fractals are geometric shapes with comparable sections; in statistical character, the complete figure, fractals can be employed in the production of structures such as landscapes or snowflakes with similar and recurring elements. These are patterns that never stop. They can also be used to explain random phenomena like fluid turbulence. Benoit Mandelbrot is recognized as being the first person to explain fractals in language (Imre & Novotny, 2016). He asserted in 1975 that they were geometric forms that, when divided into parts, resembled the shape of the whole. The name he chose for the geometric figures; that is fractals, originated from the Latin word ‘fractus’ which means ‘broken’. Fractals can be found in nature such as trees, rivers and coastlines. There are other sets of fractals that were discovered by other mathematicians. These include: Gaston Julia, Warclaw Sierpinski, Helge von Koch and Greg Cantor who all have their own set of fractals.

Star Trek is acknowledged as the first movie that applied fractals in its production in order to make the natural phenomena used in the movie to appear as realistic as possible. Fractals are an essential part in the making of computer generated images which are used in movies (Thompson & Michael, 2016). Loren Carpenter is a computer scientist whose work in the use of fractals to make computer generated images is recognized. His work included the use of small, simple shapes of triangles which when iterated ended up looking like the jagged nature of mountains. The underlying principles in fractals and their usage are fractal dimensions and self-similarity (Pant & Pant, 2013). Fractal geometry has been used in social research to explain phenomena which when studied in a micro state, replicate when the larger society is also studied. Fractal geometry has also been applied in other sectors apart from the mathematical profession; for example in fashion and the construction industry. In economics, fractal geometry has a wide range of application including the study of price changes in an open market and the study of demand and supply in a market (Bucur, 2017).

Steelberg Films is a production company which intends to apply fractal geometry in their next movie. Fractals are important to their next film, Mars Landing, as they want to include landscapes and ocean formations in the movie. In order to make the natural phenomena they want to incorporate in the movie to look as realistic as possible, they have to use fractal geometry so that even when the images are magnified in cinemas, they still look realistic. Moreover, Mars Landing will also have spaceship scenes which can produce better using fractals. As such, this paper is aimed at providing the framework in which they can use fractals to produce Mars Landing; which includes the incorporation of landscapes, spaceship scenes and ocean formations. The use of drones in filmmaking will also be discussed with the opportunities and challenges that it presents analyzed herein in order to argue for the use of fractals in the film, Mars Landing, as opposed to drone filmmaking. Finally, the social and economic opportunities of fractal geometry in society will be studied in relation to trends in filmmaking in order to advise Mike Steelberg on the best course of action.

In order to aid the conduct of this research, the background of the use of fractals in the making of films such as Star Trek is important in order to understand how the landscapes, ocean formations and spaceship scenes will be made. In the formation of landscapes and other natural phenomena, Mandelbrot opined that the variables were of the order D=1.2-1.3 whereby the effects in the long range would be the ones to dominate (Weber, 2015). The resulting fractals in the case of landscapes are shown below:

Missing variables and information may cause problems such as such as missing scales could result in chaos in the fractal images ultimately created in the film (Stauffer, Stanley, & Lesne, 2017). The issue of fractals use in the making of films is important because it affects the social and economic trends in society. This is because it enables cheaper filmmaking which results in affordable costs of buying of films or watching them in cinemas. It therefore encourages the buying of affordable films as opposed to pirating them off the internet.

Part 2: Compilation of Research, Data, or Other Pertinent Information

Fractals geometry used in the creation of landscapes, ocean formations and spaceship scenes

For landscapes, the Fast Fourier Transform algorithm should be used to create the landscape. The FFT is used to compute the Discrete Fourier Algorithm and its inverse (Dhok, Deshmukh, & Keskar, 2014). This algorithm is used in the following way: a two dimensional grid made up of random values is created; the Fast Fourier Transform is applied in two dimensions the values are then transformed by 1/fr whereby f is the frequency that the value represents and r is the parameter of roughness; and then the inverse FFT is applied thus creating the landscape. A resulting landscape image that can be created in such a manner is shown below:

The algorithm that could be used for the ocean formations in computer generated images for the film, Mars Landing, is the diamond-square algorithm which works better for height maps than the random midpoint displacement fractal, the plasma fractal and the cloud fractal. In the formation of an ocean, the algorithm to be used is 2n +1 and four corner points set at the first values to be used. Afterwards, the diamond and square steps should be repeated in alternation to ensure that all the values are in place. The value of the random number should then be reduced. For the creation of space scenes such as the one used in the movie Lucy, fractal geometry should be presented as particles on a film screen space. Each particle could then be conveyed as a ray while also ensuring that the number of particles in the final image is not interfered with despite it being a difficult task. Krakatoa and 3Ds Max can thereafter be used to make the image look like a scene from outer space (Yuan, Hui, & Zhen, 2017).

The graph below shows the economic impact of fractals as pertains to the price changes in open markets such as the filmmaking industry in which Steelberg Films will create the new film Mars Landing. This shows the fractal nature in economics with trends in price changes reoccurring with time (Mandelbrot, 2013).

The use of drones in filmmaking

Drones can also be used in the making of films instead of using fractals in order to be able to use realistic images in a film. Drones have been used in the making of movies such as the Expendables. The advantages of using drones include the fact they offer a real image which is not computer generated thereby giving a realistic feeling to the actors involved in the creation of the film; they also allow filmmakers to get exclusive footage into areas that human beings cannot access, savings in cost of getting real images, such as close-up images of volcanic eruptions which can thereafter be used in films; and their ability to maneuver in silence with minimal interference. However, the disadvantages of using drones in filming include issues on safety, the amount of regulation and bureaucracy involved in their usage and the fact that they can also be turned into weapons thereby raising safety concerns for the public. As such, there are laws prohibiting the use of drones for commercial purposes. The main point of concern when it comes to the use of drones for filmmaking in movies is the safety concerns in their use.

The data collected relates gives insight into the social and economic trends associated with filmmaking. It is notable that fractals are still the most preferred in the making of films as opposed to the use of drones although drones are increasingly becoming more desirable. However, the use of drones in filmmaking is still in the experimental stage as opposed to becoming an accepted phenomenon as fractals already are. The accuracy that is associated with fractals cannot be underestimated either.

Part 3: Problem Solving Related to this Situation

The first assumption that was used in the creation of the fractal images such as landscapes was the assumption of homogeneity. This is the assumption that there is uniform spread of matter in the natural phenomena that are created. As such, they replicate in a similar manner both on small and large scales. Although there is some replication seen in nature; fractals has also been discussed as chaos since there are differences that are sometimes seen especially when comparing large scales to small ones. However, there is also the belief that the chaos are also self-replicating thereby being homogenous.

The data collected is in support of the aim of the research which was an argument for the use of fractals in the movie, Mars Landing. This is because it would save cut production costs while also providing a safe method of acquiring the images needed for the film which would also look realistic on any level of magnification of the images. Drones were determined to be less efficient due to the regulations that make them difficult to use and also the safety issues associated with them. In this case where the movie is to have scenes of space, a use of drones would require that there is filming done in space which would create more expenses as the cameras that would have to be used in the filming of space would have to be of superior quality. It would be cheaper if fractals were used in computers to create the desired images.

The data collected and the analysis show that there are assumptions in the use of fractals which must also be considered in society. For example, due to the lowering of costs for producing the movie Mars Landing; it would be expected that many more people would be attracted by the low cost of the movie to watch it in cinemas and to buy it. However, this is based on assumptions. There is neither proof that such trends result in such expected outcomes nor that there this relates to the use of fractals in economic theories in order to explain supply and demand, for example. The relation of supply and demand to fluctuation in market prices is also critical in this study with the result being that there are fractal trends involved.

Part 4: Conclusion and Recommendations

Through the information I collected, I can infer that although drones are also effective in the development of realistic looking films, fractals are much cheaper and more efficient. This is because computer generated fractal images are exact and even when magnified on a large screen; look similar to the smaller image created.

The information that could lead me to a different conclusion would be an in depth study of the use of drones in filmmaking which has not been fully explored because of the legal stipulations that are still in place limiting the use of drones for commercial purposes. Assumptions in fractal geometry also have the ability to deter me from believing that the use of fractals is the best course of action for the movie Mars Landing because there is the possibility that the images used are not realistic as in real life, nature is not perfectly self recurring. My recommendations would be for the use of fractals as opposed to drones for making of the movie Mars Landing although a follow up study on the use of drones to produce more realistic images should be undertaken. There also needs to be a follow up study on whether good productions that are realistic attract more revenue due to better quality.

Bibliography

Bucur, A. (2017). About Applications of the Fixed Point Theory. Scientific Bulletin, 22(1) , 13-17.

Dhok, S. B., Deshmukh, R. B., & Keskar, A. (2014). Efficient fractal image coding using fast Fouriertransform. GSTF Journal on Computing (JoC), 1(2) .

Imre, A. R., & Novotny, J. (2016). Fractals and the Korcak-law: a history and a correction. The European Physical Journal H, 41(1) , 69-91.

Mandelbrot, B. B. (2013). Fractals and Scaling in Finance: Discontinuity, Concentration, Risk. Selecta Volume E. Springer Science and Business Media.

Pant, V., & Pant, P. (2013). Fractal Geometry: An Introduction. . Journal of Indian Research, 1(2) , 66-70.

Stauffer, D. H., Stanley, E., & Lesne, A. (2017). Fractals in Theoretical Physics. From Newton to Mandelbrot. Springer Berlin Heidelberg.

Thompson, J., & Michael, T. (2016). Chaos, Fractals and their Bifurcation and Chaos 26(13). International Journal of Bifurcation and Chaos , 1630035.

Weber, S. E. (2015). The Scope of Fractals: Geometry, Iteration, Application.

Yuan, Y., Hui, L., & Zhen, L. (2017). Study on the Application of CG Technology to the Creation of Short Film Works Soul Painting. In Proceedings of the 2017 International Conference on Computer Graphics and Digital Image Processing. ACM , 5.