Pentagrams for Nerds

[Onyx]

The pentagram embodies several Golden Ratios in it's geometry, making it an ideal symbol for Phi: defined mathematically as:

(1 + sqrt(5)) / 2.

1.618034 is a close enough approximation. The reciprocal is .618034, note that the fractional portion is the same either way.

There is also a mathematical relationship to Pi (3.141593) in that one may be calculated from the other:

Phi = 1 – (2 * cos((3 * Pi) / 5))

Pi = 2 * acos(Phi / 2)

In a magical context, the pentagram (with surrounding circle) represents Phi and Pi, and the (not always obvious) linkage between the two. It is up to the black magician to experiment and find useful connections between the Subjective and Objective realms (as symbolized by Phi and Pi). When inverted, the pentagram rests on a single point, representing balance in the pursuit of Xeper.

Might add more later.

 

[1137]

As far as I know, one point up is actually the upside down, inverted version.

 

[Adramelek]

When inverted, the pentagram rests on a single point, representing balance in the pursuit of Xeper.

An excellent analysis. Also, the inverted pentagram rests on a single point symbolizing the balance between the objective and subjective universes.

 

[Sutekh]

The Pentagram of Set also symbolizes the core principle of individuality as said from one of Don Webb's books.

 

[Onyx]

The Pentagram of Set also symbolizes the core principle of individuality as said from one of Don Webb's books.

I'm assuming this:

(from Uncle Setnakt's Essential Guide to the Left Hand Path)

The core level of dynamism is the unchangeable part of the Self. It
exists as an absolute pattern for potential. In many myths, the core part of
ourselves is the first land, the magical island rising from the watery
depths. Here is that part of you which is unique, indestructible, and not
directly observable - but its presence in the Cosmos sets up those
situations that cause you to become aware firstly of your own existence,
and then to sense what sorts of experiences might help with your
development. It is, in short, the reason for your unique existence, and all
furthering of its development is the Work of the Left Hand Path. It is
rarely perceived in our lives since our attention is loosely housed there.
The core level of being is not static since it contains the principle of
dynamism. The name for this core level is the Principle of Isolate
Intelligence. The Symbol for the core level of being is the Inverse
Pentagram surrounded by a circle. The core level of being provides
Individuality.

 

[Onyx]

Hehe.

// Pentagram of Set Ascii-Art generator by Onyx.

#include <stdio.h>
#include <string.h>
#include <malloc.h>

// choose size here
#define WIDTH 60
#define HEIGHT 30

static int *data;
static int **row;

static inline void swap(int *x, int *y)
{
  *x ^= *y;
  *y ^= *x;
  *x ^= *y;
}

static inline void plot(int x, int y)
{
  *(row[y] + x) = 1;  
}

static inline void hline(int x1, int y, int x2)
{
  int *x = row[y] + x2;
  int *z = row[y] + x1;

  do
  {
    *x = 1;
    x--;
  }
  while(x >= z);
}

static void line(int x1, int y1, int x2, int y2)
{
  int dx, dy, inx, iny, e;

  dx = x2 - x1;
  dy = y2 - y1;
  inx = dx > 0 ? 1 : -1;
  iny = dy > 0 ? 1 : -1;

  dx = dx > 0 ? dx : -dx;
  dy = dy > 0 ? dy : -dy;

  if(dx >= dy)
  {
    dy <<= 1;
    e = dy - dx;
    dx <<= 1;

    while(x1 != x2)
    {
      plot(x1, y1);

      if(e >= 0)
      {
        y1 += iny;
        e -= dx;
      }

      e += dy;
      x1 += inx;
    }
  }
  else
  {
    dx <<= 1;
    e = dx - dy;
    dy <<= 1;

    while(y1 != y2)
    {
      plot(x1, y1);

      if(e >= 0)
      {
        x1 += inx;
        e -= dy;
      }

      e += dx;
      y1 += iny;
    }
  }
}

static void oval(int x1, int y1, int x2, int y2)
{
  int w = (x2 - x1);
  int h = (y2 - y1);
  w = w > 0 ? w : -w;
  h = h > 0 ? h : -h;

  int x, y;
  int ex, ey;

  int a = w / 2;
  int b = h / 2;
  int a2, b2;
  int s, t;

  if(x1 > x2)
    swap(&x1, &x2);
  if(y1 > y2)
    swap(&y1, &y2);

  ex = (w & 1);
  ey = (h & 1);

  if(w <= 1 && h <= 1)
  {
    plot(x1, y1);
    plot(x1 + ex, y1);
    plot(x1, y1 + ey);
    plot(x1 + ex, y1 + ey);
    return;
  }

  if(h <= 0 && w >= 0)
  {
    hline(x1, y1, x2);
    return;
  }

  x1 += a;
  y1 += b;

  a2 = a * a;
  b2 = b * b;

  x = 0;
  y = b;

  s = a2 * (1 - 2 * b) + 2 * b2;
  t = b2 - 2 * a2 * (2 * b - 1);

  plot(x1 + x + ex, y1 + y + ey);
  plot(x1 - x, y1 + y + ey);
  plot(x1 - x, y1 - y);
  plot(x1 + x + ex, y1 - y);

  do
  {
    if(s < 0)
    {
      s += 2 * b2 * (2 * x + 3);
      t += 4 * b2 * (x + 1);
      x++;
    }
    else
    {
      if(t < 0)
      {
        s += 2 * b2 * (2 * x + 3) - 4 * a2 * (y - 1);
        t += 4 * b2 * (x + 1) - 2 * a2 * (2 * y - 3);
        x++;
        y--;
      }
      else
      {
        s -= 4 * a2 * (y - 1);
        t -= 2 * a2 * (2 * y - 3);
        y--;
      }
    }

    plot(x1 + x + ex, y1 + y + ey);
    plot(x1 - x, y1 + y + ey);
    plot(x1 - x, y1 - y);
    plot(x1 + x + ex, y1 - y);
  }
  while(y > 0);

  hline(x1 - w / 2, y1, x1 - x);
  hline(x1 + x + ex, y1, x1 + w / 2 + ex);

  if(ey)
  {
    hline(x1 - w / 2, y1 + 1, x1 - x);
    hline(x1 + x + ex, y1 + 1, x1 + w / 2 + ex);
  }
}

int main()
{
  int x, y, i;

  // pentagram vertices
  static double px[6] = { .305, 0, -.305, .494, -.494, .305 };
  static double py[6] = { -.418, .520, -.418, .162, .162, -.418 };

  // data structure stuff
  data = malloc(sizeof(int) * WIDTH * HEIGHT);
  row = malloc(sizeof(int *) * HEIGHT);
  memset(data, 0, sizeof(data));

  for(i = 0; i < HEIGHT; i++)
    row[i] = &data[WIDTH * i];

  int cx = WIDTH / 2;
  int cy = HEIGHT / 2;

  // scale pentagram
  int rx = cx * 1.5;
  int ry = cy * 1.5;

  // draw pentagram
  for(i = 0; i < 5; i++)
  {
    line(cx + rx * px[i + 0], cy + ry * py[i + 0],
         cx + rx * px[i + 1], cy + ry * py[i + 1]);
  }

  // draw circle
  oval(0, 0, WIDTH - 1, HEIGHT - 1);

  // output to screen
  putchar('\n');

  for(y = 0; y < HEIGHT; y++)
  {
    for(x = 0; x < WIDTH; x++)
    {
      if(*(row[y] + x) == 1)
        putchar('*');
      else
        putchar(' ');
    }

    putchar('\n');
  }

  free(row);
  free(data);

  return 0;
}

 

[Aštra’el]

The pentagram that has the most meaning for me is a pentagram rotated so that it is pointing neither "up" or "down", with another pentagram within it. It is a symbol I use to represent a microcosm within a Macrocosm, as well as the interior universe within us and the exterior universe around us. Being neither inverted or "right side up", it also represents for me the clarity that comes when perceiving things from an amoral perspective.

 

[Onyx]

The pentagram that has the most meaning for me is a pentagram rotated so that it is pointing neither "up" or "down", with another pentagram within it. It is a symbol I use to represent a microcosm within a Macrocosm, as well as the interior universe within us and the exterior universe around us. Being neither inverted or "right side up", it also represents for me the clarity that comes when perceiving things from an amoral perspective.

Something like this maybe?