In this post, we will see some of the nice mysteries around the mathematical patterns of the universe. We will see the relationship between energy, frequency and vibration. According to Universal law, everything vibrates at some frequency. Sound is also a vibration and so are thoughts. Everything that manifests itself in your life is there because it matches the vibration from your thoughts.
Some of the special frequencies are:

Earth’s natural frequency, 7.83 Hz (7 + 8 + 3 = 18 = 1 + 8 = 9)

Turning Grief into Joy, Liberating Guilt & Fear, 396 Hz (3 + 9 + 6 = 18 = 1 + 8 = 9)

Undoing Situations & Facilitating Change (Renewal), 417 Hz (4 + 1 + 7 = 12 = 1 + 2 = 3)

Universal Frequency, 432 Hz (4 + 3 + 2 = 9) – The frequency of 432 Hz vibrates on the principle of golden mean \( \Phi \) and unifies the peroperties of space, time, light, gravity and matter and magentism with biology DNA code and consciouness.

Love, Transformation, Miracles and DNA repair, 528 Hz (5 + 2 + 8 = 15 = 1 + 5 = 6)

Reconnecting relationships, 639 Hz (6 + 3 + 9 = 18 + 1 + 8 = 9)

Awakening Intuition, returning to spiritual order, 852 Hz (8 + 5 + 2 = 15 = 1 + 5 = 6)

God’s frequency, 963 Hz (9 + 6 + 3 = 18 = 1 + 8 = 9)
Lower the frequency, the denser or lower is the energy, the more problems you would see. The problems could be related to physical or emotional. Higher the frequency, the lighter or higher is the energy. You would see less of the problems that you face in when you were having lower frequency. So, ideally, one would want to make sure that physical body and mind is vibrating at high frequency or is attracted to things vibrating at high frequency. Every emotion also consists of vibrating at some stated frequency and the experience of an emotion can decrease or increase the frequency.
Frequency is expressed as Hertz (Hz), which implies one cycle per second. Solfeggio frequencies are mathematically consistent with the patterns of our universe and based on maths of adding the digits of each of these frequency we usully encountered 3, 6 and 9 which has holds a special mathematical significance as seen in the section comprising of vortex maths.
Vortex Maths
The idea of vortex maths has been contributed by scientist Marko Rodin. This describes that everything in the physical world follows a mathematical pattern of numbers – 1, 2, 4, 8, 7 and 5 and this keeps on repeating itself.
Consider the following example of calculation, starting with the number 1.
\[\begin{align*} 1 + 1 &= 2 \\ 2 + 2 & = 4 \\ 4 + 4 &= 8 \\ 8 + 8 &=16 = 1 + 6 = 7 \\ 16 + 16 &= 32 = 3 + 2 = 5, \qquad \text{we can also do } 7 + 7 = 14 = 1 + 4 = 5 \\ 32 + 32 &= 64 = 6 + 4 = 10 = 1 + 0 = 1\\ 64 + 64 &= 128 = 1 + 2 + 8 = 11 = 1 + 1 = 2 \end{align*}\]Now, if we do halving beginning with the number 1, we will get the pattern but in reverse order as shown below:
\[\begin{align*} 1 / 2 &= 0.5 = 0 + 5 = 5 \\ 0.5 / 2 &= 0.25 = 0 + 2 + 5 = 7 \\ 0.25 / 2 &= 0.125 = 0 + 1 + 2 + 5 = 8 \\ 0.125 / 2 & = 0.0625 = 0 + 0 + 6 + 2 + 5 = 13 = 1 + 3 = 4 \\ 0.0625 / 2 &= 0.03125 = 0 + 0 + 3 + 1 + 2 + 5 = 11 = 1 + 1 = 2 \\ 0.03125 / 2 &= 0.015625 = 0 + 0 + 1 + 5 + 6 + 2 + 5 = 19 = 1 + 9 = 10 = 1 + 0 = 1 \end{align*}\]The numbers 3, 6 and 9 doesn’t belong to the physical world, but are regarded as the driving force that governs the numbers of the physical world. Now, consider the numbers 3 and 6 as shown below:
\[\begin{align*} 3 + 3 &= 6 \\ 6 + 6 &= 12 = 1 + 2 = 3 \\ 12 + 12 &= 24 = 2 + 4 = 6 \\ 24 + 24 &= 48 = 4 + 8 = 12 = 1 + 2 = 3 \end{align*}\]Similarly, if you do halving as the following:
\[\begin{align*} 3 / 2 &= 1.5 = 1 + 5 = 6 \\ 1.5 / 2 &= 0.75 = 0 + 7 + 5 = 12 + 1 + 2 = 3 \\ 0.75 / 2 &= 0.375 = 0 + 3 + 7 + 5 = 15 + 1 + 5 = 6 \end{align*}\]This implies if we do doubling or halving of the numbers 3 and 6, it keeps on oscillating back and forth and keeps generating of 3 and 6.
Now, consider the number that can be regarded that doesn’t follow any pattern as can be seen below:
\[\begin{align*} 9 + 9 &= 18 = 1+ 8 = 9 \\ 18 + 18 &= 36 = 3 + 6 = 9 \\ 36 + 36 &= 72 = 7 + 2 = 9 \\ 72 + 72 &= 144 = 1 + 4 + 4 = 9 \end{align*}\]This implies that the number 9 keeps repeating itself. We can do the similar halving of 9 and it will keep generating 9.
Golden Ratio and Fibonacci Sequence
The Fibonacci sequence is \( 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, \dots \) and so on. Here, each number is the sum of the previous two number.
The golden ratio is the mathematical number which is represented as 1.618. Two quantities \( a \) and \( b \) are said to be in golden ratio \( \phi \) if
\[ \frac{a}{b} = \frac{a+b}{a} = \phi \]
Going forward in the fibonacci sequence, if we divide any two successive numbers, then the ratio converges to 1.618.
Euler’s Identity
Euler’s Identity is the most beaultiful mathematical equation and is written as:
\[ e^{i\pi} + 1 = 0 \]
It involves the 5 mathematical constants, \( e, i, \pi , 1, 0 \), that forms the basis of relationship between real and imginary number in a way that results in nothing. The mathematical constants that are involved in the equation are:

\( e \) – the base of natural algorithms, \(log_e \). The constant \(e = 2.718281828459 \) and it indicates the idea of exponential growth.

\( i \) – represents the imaginary number.

\( \pi \) – represents the irrational number that is defined as the ratio of circumference and \( 2 \pi \) of the circle.

\( 1\) – multiplicative identitiy and basis of all other numbers.

\(0 \) – represents nothingness.
Chaos Theory
Chaos theory deals with the study of chaos or deterministic chaos as it concerns deterministic nonlinear dynamical system that exhibits apparent randomness, but within the randomness there are structured patterns and recognizable structures. If there is slight variation or change in some current state of such a system, then it can produce drastic change in expected results at some later state. This inherently makes it impossible to predict the longterm behavior of such system. Some of the common example of such systems are climate behaviour, population dynamics, stock market patterns.
In the words of Edward Lorenz, chaos theory is best summarized as:
When the present determines the future, but the approximate present does not approximately determine the future.
There is an underlying butterfly effect principle in chaos which states that in a deterministic nonlinear system at any change in one state can lead to large differences in a later state. This implies that there is an exhibited behavior by the system that is sensitive dependence on initial conditions. A metaphor that best describes this behavior is – a butterfly flapping its wings in Texas can cause a hurricane in China.
Logistic Map
Logistic map describes the chaotic behavior of the population growth by a nonlinear difference equation written as:
\[ x_{n + 1} = r x_n (1  x_n) \]
where \(n = 0, 1, 2, 3, \dots \). Here, \( x_n \) represents a number between 0 and 1 which indicates the ratio of existing population to the maximum possible population. Here, \(0 < r < 4\) represents the reproduction rate.