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Space Filling Curves
Staňo, Marek ; Švub, Miroslav (referee) ; Šiler, Ondřej (advisor)
The objective of my work is introduce space filling curves, and try to generalize them to multidimensional spaces. Below are in the work informations about recursive and non-recursive solving of these curves, and usage curves in practice. The main objective is to create program which can draw these curves. Based on theory and practical knowledge I design program, which can compute the coordinates of the curve, and another program which uses these coordinates to draw the curve. To make this I will use programming language C and graphics library Gd.
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Algorithms for computation of the dimensions of state space attractors
Götthans, Tomáš ; Slanina, Martin (referee) ; Petržela, Jiří (advisor)
The geometry of chaotic attractors can be complex and difficult to describe without some mathematical tool. The topic of this contribution is the realization of program for computing the dimensions of state space attractors. We can also find out if the system is highly sensitive to initial conditions. First we need to numerically integrate system of equations, create a data set and finally we can estimate the capacity or Kaplan-Yorke dimension. The main objective of derived program is to analyze and determine chaotic behavior providing a chance to discuss the accuracy of computation engine and theoretical value.
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Space Filling Curves
Staňo, Marek ; Švub, Miroslav (referee) ; Šiler, Ondřej (advisor)
The objective of my work is introduce space filling curves, and try to generalize them to multidimensional spaces. Below are in the work informations about recursive and non-recursive solving of these curves, and usage curves in practice. The main objective is to create program which can draw these curves. Based on theory and practical knowledge I design program, which can compute the coordinates of the curve, and another program which uses these coordinates to draw the curve. To make this I will use programming language C and graphics library Gd.
|
|
|
Algorithms for computation of the dimensions of state space attractors
Götthans, Tomáš ; Slanina, Martin (referee) ; Petržela, Jiří (advisor)
The geometry of chaotic attractors can be complex and difficult to describe without some mathematical tool. The topic of this contribution is the realization of program for computing the dimensions of state space attractors. We can also find out if the system is highly sensitive to initial conditions. First we need to numerically integrate system of equations, create a data set and finally we can estimate the capacity or Kaplan-Yorke dimension. The main objective of derived program is to analyze and determine chaotic behavior providing a chance to discuss the accuracy of computation engine and theoretical value.
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