I would like to add some explorations of the concept asked by the OP of my own:

1. Visualization of the set of real roots of quadratic equations $ax^2+bx+c=0$, for the specific values of the intervals $a \in [-a_i,a_i]$, $b \in [-b_i,b_i]$, $c \in [-c_i,c_i]$, $a,b,c \in \Bbb N$.

By Cartesian coordinates $(x,y)=(x_1,x_2)$. E.g. $a_i,b_i,c_i=75$:

By Polar coordinates $(\theta, r)=(x_1,x_2)$. E.g. $a_i,b_i,c_i=75$:

Due to the symmetries the opposite patterns $(x,y)=(x_2,x_1)$ and $(\theta,r)=(x_2,x_1)$ are similar.

2. The Chaos Game on the metric space $S^{1} \times [0,\infty)$ with the metric $d((\theta_1,x_1),(\theta_2,x_2)) = d_{S^1}(\theta_1,\theta_2) + |x_1-x_2|$. The distance in $S^1$ is given by the smallest angle measure between $\theta_1$ and $\theta_2$ (this is actually a scaled Euclidean metric on the unit circle itself).

In this version, the points are $(\theta, r)$, (the angle in radians and the radius). And the three attractor points are $A=(0,0)$,$B=(\frac{5\pi}{4},1)$ and $C=(\frac{7\pi}{4},10^4)$.

This is another example locating the attractor points in the same axis: $A=(0,0)$,$B=(\pi-\frac{\pi}{8},1)$ and $C=(\frac{7\pi}{4},10^4)$.

3. Contruction step by step of the Voronoi diagram of the points generated by a classic Chaos Game Sierpinski gasket.

4. And my favorite so far, visualization of the $4$-tuples of the extended Euclidean algorithm in a four dimensional tesseract. The projection of the four dimensional points are shown into a $3D$ visualization adding as a reference a tesseract or hypercube:

I would like to add some explorations of the concept asked by the OP of my own:

1. Visualization of the set of real roots of quadratic equations $ax^2+bx+c=0$, for the specific values of the intervals $a \in [-a_i,a_i]$, $b \in [-b_i,b_i]$, $c \in [-c_i,c_i]$, $a,b,c \in \Bbb N$.

By Cartesian coordinates $(x,y)=(x_1,x_2)$. E.g. $a_i,b_i,c_i=75$:

By Polar coordinates $(\theta, r)=(x_1,x_2)$. E.g. $a_i,b_i,c_i=75$:

Due to the symmetries the opposite patterns $(x,y)=(x_2,x_1)$ and $(\theta,r)=(x_2,x_1)$ are similar.

2. The Chaos Game on the metric space $S^{1} \times [0,\infty)$ with the metric $d((\theta_1,x_1),(\theta_2,x_2)) = d_{S^1}(\theta_1,\theta_2) + |x_1-x_2|$. The distance in $S^1$ is given by the smallest angle measure between $\theta_1$ and $\theta_2$ (this is actually a scaled Euclidean metric on the unit circle itself).

In this version, the points are $(\theta, r)$, (the angle in radians and the radius). And the three attractor points are $A=(0,0)$,$B=(\frac{5\pi}{4},1)$ and $C=(\frac{7\pi}{4},10^4)$.

This is another example locating the attractor points in the same axis: $A=(0,0)$,$B=(\pi-\frac{\pi}{8},1)$ and $C=(\frac{7\pi}{4},10^4)$.

3. Contruction step by step of the Voronoi diagram of the points generated by a classic Chaos Game Sierpinski gasket.

4. And my favorite so far, visualization of the $4$-tuples of the extended Euclidean algorithm in a four dimensional tesseract. The projection of the four dimensional points are shown into a $3D$ visualization adding as a reference a tesseract or hypercube:

I would like to add some explorations of the concept asked by the OP of my own:

1. Visualization of the set of real roots of quadratic equations $ax^2+bx+c=0$, for the specific values of the intervals $a \in [-a_i,a_i]$, $b \in [-b_i,b_i]$, $c \in [-c_i,c_i]$, $a,b,c \in \Bbb N$.

By Cartesian coordinates $(x,y)=(x_1,x_2)$. E.g. $a_i,b_i,c_i=75$:

By Polar coordinates $(\theta, r)=(x_1,x_2)$. E.g. $a_i,b_i,c_i=75$:

Due to the symmetries the opposite patterns $(x,y)=(x_2,x_1)$ and $(\theta,r)=(x_2,x_1)$ are similar.

2. The Chaos Game on the metric space $S^{1} \times [0,\infty)$ with the metric $d((\theta_1,x_1),(\theta_2,x_2)) = d_{S^1}(\theta_1,\theta_2) + |x_1-x_2|$. The distance in $S^1$ is given by the smallest angle measure between $\theta_1$ and $\theta_2$ (this is actually a scaled Euclidean metric on the unit circle itself.

In this version, the points are $(\theta, r)$, (the angle in radians and the radius). And the three attractor points are $A=(0,0)$,$B=(\frac{5\pi}{4},1)$ and $C=(\frac{7\pi}{4},10^4)$.

This is another example locating the attractor points in the same axis: $A=(0,0)$,$B=(\pi-\frac{\pi}{8},1)$ and $C=(\frac{7\pi}{4},10^4)$.

3. Contruction step by step of the Voronoi diagram of the points generated by a classic Chaos Game Sierpinski gasket.

4. And my favorite so far, visualization of the $4$-tuples of the extended Euclidean algorithm in a four dimensional tesseract. The projection of the four dimensional points are shown into a $3D$ visualization adding as a reference a tesseract or hypercube:

I would like to add some explorations of the concept asked by the OP of my own:

1. Visualization of the set of real roots of quadratic equations $ax^2+bx+c=0$, for the specific values of the intervals $a \in [-a_i,a_i]$, $b \in [-b_i,b_i]$, $c \in [-c_i,c_i]$, $a,b,c \in \Bbb N$.

By Cartesian coordinates $(x,y)=(x_1,x_2)$. E.g. $a_i,b_i,c_i=75$:

By Polar coordinates $(\theta, r)=(x_1,x_2)$. E.g. $a_i,b_i,c_i=75$:

Due to the symmetries the opposite patterns $(x,y)=(x_2,x_1)$ and $(\theta,r)=(x_2,x_1)$ are similar.

2. The Chaos Game on the metric space $S^{1} \times [0,\infty)$ with the metric $d((\theta_1,x_1),(\theta_2,x_2)) = d_{S^1}(\theta_1,\theta_2) + |x_1-x_2|$. The distance in $S^1$ is given by the smallest angle measure between $\theta_1$ and $\theta_2$ (this is actually a scaled Euclidean metric on the unit circle itself).

In this version, the points are $(\theta, r)$, (the angle in radians and the radius). And the three attractor points are $A=(0,0)$,$B=(\frac{5\pi}{4},1)$ and $C=(\frac{7\pi}{4},10^4)$.

This is another example locating the attractor points in the same axis: $A=(0,0)$,$B=(\pi-\frac{\pi}{8},1)$ and $C=(\frac{7\pi}{4},10^4)$.

3. Contruction step by step of the Voronoi diagram of the points generated by a classic Chaos Game Sierpinski gasket.

4. And my favorite so far, visualization of the $4$-tuples of the extended Euclidean algorithm in a four dimensional tesseract. The projection of the four dimensional points are shown into a $3D$ visualization adding as a reference a tesseract or hypercube: