n Radius of added spheres Number of added spheres Volume of added spheres Aera of added spheres
0 $$R_{ini}$$ 1 $$\frac{4\pi \cdot R^{3}}{3}$$ $$4\pi \cdot R^{2}$$
1 $$\frac{R}{2}$$ $$6$$ $$6 \cdot 5^{0} \cdot \frac{4\pi \cdot (\frac{R}{2})^{3}}{3}$$ $$6 \cdot 4\pi \cdot (\frac{R}{2})^{2}$$
2 $$\frac{R}{2^{2}}$$ $$6 \cdot 5^{1} $$ $$6 \cdot 5^{1} \cdot \frac{4\pi \cdot (\frac{R}{2^{2}})^{3}}{3}$$ $$6 \cdot 5^{1} \cdot 4\pi \cdot (\frac{R}{2^{2}})^{2}$$
3 $$\frac{R}{2^{3}}$$ $$6 \cdot 5^{2} $$ $$6 \cdot 5^{2} \cdot \frac{4\pi \cdot (\frac{R}{2^{3}})^{3}}{3}$$ $$6 \cdot 5^{2} \cdot 4\pi \cdot (\frac{R}{2^{3}})^{2}$$
4 $$\frac{R}{2^{4}}$$ $$6 \cdot 5^{3} $$ $$6 \cdot 5^{3} \cdot \frac{4\pi \cdot (\frac{R}{2^{4}})^{3}}{3}$$ $$6 \cdot 5^{3} \cdot 4\pi \cdot (\frac{R}{2^{4}})^{2}$$
5 $$\frac{R}{2^{5}}$$ $$6 \cdot 5^{4} $$ $$6 \cdot 5^{4} \cdot \frac{4\pi \cdot (\frac{R}{2^{5}})^{3}}{3}$$ $$6 \cdot 5^{4} \cdot 4\pi \cdot (\frac{R}{2^{5}})^{2}$$
6 $$\frac{R}{2^{6}}$$ $$6 \cdot 5^{5} $$ $$6 \cdot 5^{5} \cdot \frac{4\pi \cdot (\frac{R}{2^{6}})^{3}}{3}$$ $$6 \cdot 5^{5} \cdot 4\pi \cdot (\frac{R}{2^{6}})^{2}$$

The rule to find the volume of the fractal until iteration i will be : $$\frac{4\pi \cdot R^{3}}{3} + \sum_{n=1}^{i} \frac{24\pi \cdot 5^{n-1} \cdot R^{3}}{3\cdot2^{3n}}$$

The rule to find the surface area of the fractal until iteration i will be : $$4\pi \cdot R^{2} + \sum_{n=1}^{i} 24\pi \cdot 5^{n-1} \cdot \frac{R^{2}}{2^{2n}} $$

Give the number of iteration and the initial radius and it will calculate the volume and the surface area of the fractal at that iteration.
i: iterations
r: units
Volume: units3
Aera: units2