# Tagged Questions

Questions on fractals, irregular-looking mathematical objects that display the property of self-similarity.

178 views

### Has this chaotic map been studied?

I have recently been playing around with the discrete map $$z_{n+1} = z_n - \frac{1}{z_n}$$ That is, repeatedly mapping each number to the difference between itself and its reciprocal. It shows some ...
415 views

### Visualizing the Partition numbers (suggestions for visualization techniques)

So Ken Ono says that the partition numbers behave like fractals, in which case I'd like to try to find an appropriately illuminating way of visualizing them. But I'm sort of stuck at the moment, so ...
199 views

### Pythagoras tree bounding size

The Pythagoras tree is a fractal generated by squares. For each square, two new smaller squares are constructed and connected by their corners to the original square. The angle of the triangle formed ...
90 views

74 views

### Fractal identification

I was trying different algorithms out, and after a while, I found this fractal: The generation has similarities to Koch's curve, but instead of putting triangles on triangles, I put circles on top ...
155 views

131 views

### The Tribonacci constant and the Dragon

Let $x = \frac{\ln T}{\ln 2} = 0.879146\dots$ where $T$ is the tribonacci constant, then x solves the transcendental equation, $$4^x(2^x-1)=(2^x+1)$$ Let $x = \frac{\ln y}{\ln 2} = 1.523627\dots$ ...
123 views

### Help understanding this 'Fractal' I've just made?

I was messing around in C++, making an image where the pixels change depending on the the rectangle's dimensions and whether or not the space bar is down, and I formed this image: Could anyone ...
246 views

### Mandelbrot set's border in parametric form

I've post this question just because I'm curious, Mandelbrot set is defined as: $z_{n+1} = z^2_n + c$, if $n \rightarrow \infty$ and it doesn't diverge we get the border. This border is unlimited ...
208 views

113 views

### What is asymptotics of this oscillatory double sum? (Fractal Dimension problem)

The term Gibbs Phenomenon refers to the peculiar way Fourier Series behave at sharp changes in a function's value. However, this problem becomes particularly annoying to deal with when trying to ...
87 views

### Is it known whether the boundary of the Mandelbrot set is not continuous?

I might be missing something obvious here, but my understanding is that nobody currently knows whether the boundary of the Mandelbrot set is a Jordan curve because otherwise we would know that the ...
131 views