- #1

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for example Sierpinski-triangle,

made of material with homogeneous conductivity.

What do you think,

it has zero, finite, or infinite resistance between two points

(for example two corner of the triangle)?

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- Thread starter mersecske
- Start date

- #1

- 186

- 0

for example Sierpinski-triangle,

made of material with homogeneous conductivity.

What do you think,

it has zero, finite, or infinite resistance between two points

(for example two corner of the triangle)?

- #2

- 4,254

- 1

The resistance at each point contact of one triangle to another is infinite. Recursing from the zeroth single to the first order the resistance is infinity at every contact. Every subsequent order gets the same, ad infinitium it seems.

You should be aware that, given any infinite plan or volume of material having nonzero resistivity, the resistance between any two*ideal* point contacts is infinite resistance. In real life, Ohm meter probes do not contact at an idealized point, but over an area. It is the contact parimeter of the probes that dictates the reading on a DVM rather than the resistivity of the material, beyond the kin of the electrical engineers who normally specify such sorts of measurements.

You should be aware that, given any infinite plan or volume of material having nonzero resistivity, the resistance between any two

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- #3

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But what about the resistance between

oposite sides of a Menger sponge?

Its existed and finite?

- #4

- 4,254

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- #5

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And not possible to measure :)

And the contacts are still not clear!

Maybe we have to take infinite wire with fractal cross section

?

- #6

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I presumed you intended to pick opposite faces of the cube. For your zeroth order unit cube the contact area is one unit square. The sequence for the contact area is (1, 9/10, 81/100...).

- #7

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Yes but the current flow is very difficult

- #8

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- #9

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Do you now what is fractal?

The fractal has finite surface!

Only its circumference is infinity.

The fractal has finite surface!

Only its circumference is infinity.

- #10

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But I see I made an error in my last post. I meant to say "If you know your contact areas tends to

Anyway, this is the case with your fractal, and so the resistance for a finite cube is automatically infinite. The series 1, 9/10, 81/100 ... tends to zero.

- #11

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The series (8/9)^n, but yes.

- #12

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