• Corpus ID: 233024942

On Fractal Features and Fractal Linear Space About Fractal Continuous Functions

@inproceedings{Xiao2021OnFF,
  title={On Fractal Features and Fractal Linear Space About Fractal Continuous Functions},
  author={Wei Xiao},
  year={2021}
}
  • W. Xiao
  • Published 4 April 2021
  • Mathematics
This paper investigates fractal dimension of linear combination of fractal continuous functions with the same or different fractal dimensions. It has been proved that: (1) BVI all fractal continuous functions with bounded variation is fractal linear space; (2) DI all fractal continuous functions with Box dimension one is a fractal linear space; (3) DI all fractal continuous functions with identical Box dimension s(1 < s ≤ 2) is surprisingly a non-fractal linear space, even non-fractal linear… 

References

SHOWING 1-10 OF 32 REFERENCES
PROGRESS ON ESTIMATION OF FRACTAL DIMENSIONS OF FRACTIONAL CALCULUS OF CONTINUOUS FUNCTIONS
In this paper, fractal dimensions of fractional calculus of continuous functions defined on [Formula: see text] have been explored. Continuous functions with Box dimension one have been divided into
FRACTAL DIMENSIONS OF LINEAR COMBINATION OF CONTINUOUS FUNCTIONS WITH THE SAME BOX DIMENSION
In this paper, we mainly discuss continuous functions with certain fractal dimensions on [Formula: see text]. We find space of continuous functions with certain Box dimension is not closed.
Fractal dimensions of fractional integral of continuous functions
In this paper, we mainly explore fractal dimensions of fractional calculus of continuous functions defined on closed intervals. Riemann–Liouville integral of a continuous function f(x) of order v(v >
Fractal dimension of Riemann-Liouville fractional integral of 1-dimensional continuous functions
Abstract The present paper investigates fractal dimension of fractional integral of continuous functions whose fractal dimension is 1 on [0, 1]. For any continuous functions whose Box dimension is 1
Box dimension and fractional integral of linear fractal interpolation functions
On the Weierstrass-Mandelbrot fractal function
  • M. Berry, Z. V. Lewis, J. Nye
  • Mathematics
    Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1980
The function W(t)≡∑n=−∞∞[(1−eiγnt)eiϕn]γ(2−D)n(11,ϕn=arbitraryphases) is continuous but non-differentiable and possesses no scale. The graph of ReW or Im W has Hausdorff-Besicovitch (fractal)
DEFINITION AND CLASSIFICATION OF ONE-DIMENSIONAL CONTINUOUS FUNCTIONS WITH UNBOUNDED VARIATION
The present paper mainly investigates the definition and classification of one-dimensional continuous functions on closed intervals. Continuous functions can be classified as differentiable functions
The Hausdorff dimension of graphs of Weierstrass functions
The Weierstrass nowhere differentiable function, and functions constructed from similar infinite series, have been studied often as examples of functions whose graph is a fractal. Though there is a
Some remarks on one-dimensional functions and their Riemann-Liouville fractional calculus
A one-dimensional continuous function of unbounded variation on [0, 1] has been constructed. The length of its graph is infinite, while part of this function displays fractal features. The Box
The box dimension of self-affine graphs and repellers
The box dimension (or 'capacity') of a class of self-affine sets in the plane is calculated. The formula for box dimension given here has a similar form to Bowen's formula for the Hausdorff dimension
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