Length of Koch Curve after n Iterations Calculator

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✖The Number of Iterations of Koch Curve is the number of steps completed during the process of iteration in the formation of Koch Curve.ⓘ Number of Iterations of Koch Curve [n]			+10% -10%
✖The Initial Length of Koch Curve is the length of the curve which undergoing iteration to form the Koch Curve of respective iteration order.ⓘ Initial Length of Koch Curve [l₀]			+10% -10%

✖The Length of Koch Curve after n Iterations is the length of Koch Curve after completing n number of iterations on the original or initial length.ⓘ Length of Koch Curve after n Iterations [l_n]

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Formula

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Length of Koch Curve after n Iterations

Formula

`"l"_{"n"} = (4/3)^"n"*"l"_{"0"}`

Example

`"64m"=(4/3)^"3"*"27m"`

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Length of Koch Curve after n Iterations Solution

STEP 0: Pre-Calculation Summary

Formula Used

Length of Koch Curve after n Iterations = (4/3)^Number of Iterations of Koch Curve*Initial Length of Koch Curve
l_n = (4/3)^n*l₀
This formula uses 3 Variables

Variables Used

Length of Koch Curve after n Iterations - (Measured in Meter) - The Length of Koch Curve after n Iterations is the length of Koch Curve after completing n number of iterations on the original or initial length.
Number of Iterations of Koch Curve - The Number of Iterations of Koch Curve is the number of steps completed during the process of iteration in the formation of Koch Curve.
Initial Length of Koch Curve - (Measured in Meter) - The Initial Length of Koch Curve is the length of the curve which undergoing iteration to form the Koch Curve of respective iteration order.

STEP 1: Convert Input(s) to Base Unit

Number of Iterations of Koch Curve: 3 --> No Conversion Required
Initial Length of Koch Curve: 27 Meter --> 27 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_n = (4/3)^n*l₀ --> (4/3)^3*27

Evaluating ... ...

l_n = 64

STEP 3: Convert Result to Output's Unit

64 Meter --> No Conversion Required

FINAL ANSWER

64 Meter <-- Length of Koch Curve after n Iterations

(Calculation completed in 00.006 seconds)

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Created by Jaseem K

IIT Madras (IIT Madras), Chennai

Jaseem K has created this Calculator and 100+ more calculators!

Verified by Nikita Kumari

The National Institute of Engineering (NIE), Mysuru

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< 5 Koch Curve Calculators

Number of Iterations of Koch Curve given Length after n Iterations

Go Number of Iterations of Koch Curve = (ln(Length of Koch Curve after n Iterations/Initial Length of Koch Curve))/(ln(4/3))

Initial Line Length of Koch Curve given Length after n Iterations

Go Initial Length of Koch Curve = (3/4)^Number of Iterations of Koch Curve*Length of Koch Curve after n Iterations

Length of Koch Curve after n Iterations

Go Length of Koch Curve after n Iterations = (4/3)^Number of Iterations of Koch Curve*Initial Length of Koch Curve

Initial Line Length of Koch Curve given Height

Go Initial Length of Koch Curve = 2*sqrt(3)*Height of Koch Curve

Height of Koch Curve

Go Height of Koch Curve = sqrt(3)/6*Initial Length of Koch Curve

Length of Koch Curve after n Iterations Formula

Length of Koch Curve after n Iterations = (4/3)^Number of Iterations of Koch Curve*Initial Length of Koch Curve
l_n = (4/3)^n*l₀

What is a Koch Curve?

The Koch curve is built by dividing a line into three equal segments, putting an equilateral triangle above the middle segment and removing the bottom line of this. This is repeated with the four new lines, and so on, infinitely. This makes the Koch curve a fractal with the Hausdorff dimension ln(4)/ln(3)≈1,26186 and infinite length.
The single steps are called iterations.

How to Calculate Length of Koch Curve after n Iterations?

Length of Koch Curve after n Iterations calculator uses Length of Koch Curve after n Iterations = (4/3)^Number of Iterations of Koch Curve*Initial Length of Koch Curve to calculate the Length of Koch Curve after n Iterations, The Length of Koch Curve after n Iterations formula is defined as the total length of the Koch Curve from one end to another end after completing n number of iterations. Length of Koch Curve after n Iterations is denoted by l_n symbol.

How to calculate Length of Koch Curve after n Iterations using this online calculator? To use this online calculator for Length of Koch Curve after n Iterations, enter Number of Iterations of Koch Curve (n) & Initial Length of Koch Curve (l₀) and hit the calculate button. Here is how the Length of Koch Curve after n Iterations calculation can be explained with given input values -> 64 = (4/3)^3*27.

FAQ

What is Length of Koch Curve after n Iterations?

The Length of Koch Curve after n Iterations formula is defined as the total length of the Koch Curve from one end to another end after completing n number of iterations and is represented as l_n = (4/3)^n*l₀ or Length of Koch Curve after n Iterations = (4/3)^Number of Iterations of Koch Curve*Initial Length of Koch Curve. The Number of Iterations of Koch Curve is the number of steps completed during the process of iteration in the formation of Koch Curve & The Initial Length of Koch Curve is the length of the curve which undergoing iteration to form the Koch Curve of respective iteration order.

How to calculate Length of Koch Curve after n Iterations?

The Length of Koch Curve after n Iterations formula is defined as the total length of the Koch Curve from one end to another end after completing n number of iterations is calculated using Length of Koch Curve after n Iterations = (4/3)^Number of Iterations of Koch Curve*Initial Length of Koch Curve. To calculate Length of Koch Curve after n Iterations, you need Number of Iterations of Koch Curve (n) & Initial Length of Koch Curve (l₀). With our tool, you need to enter the respective value for Number of Iterations of Koch Curve & Initial Length of Koch Curve and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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