FRACTAL MODELLING

(QUICK BASIC STUFF ON THE MATH AND COMPUTERS)

WHAT IS A FRACTAL ? IM RELIABLY TOLD IT MEANS FRACTIONAL GEOMETRY ( I HOPE!). IT WORKS ON THE CONCEPT OF INSTEAD OF SAY 2 OR 3 DIMENSIONS YOU CALACULATE IT AT SAY 2 AND A HALF. BUT ANYWAY HOWS IT DONE AND WHY DOES IT MATTER. THE MAJORITY OF SHAPES AROUND YOU ARE FRACTAL BASED IN SONE WAY INCLUDING YOUR BRAIN RECOGNITION, WHERE IT JUST WORKS AT RIGHT ANGLES LIKE IF WE DRAW A LINE ON A BIT OF PAPER AND THEN MAKE A SQUARE. HOW COME THERES CURVES, ILL SHOW YOU LATER ON AS USUAL BUT IT REALLY DONE BY JUST MAKING THE RIGHT ANGLES SMALLER TILL YOU CANT SEE THEM ANYMORE.

THATS WHY THERES A TREE ON THE PICTURE ON ENTRY TOO THE PAGE, ITS A FRACTAL BRANCH STRUCTURE, ITS THE SAME REALLY AS LIGHTNING , BLOOD VESSELS, THE LITTLE VEIN TYPE STRUCTURES IN LEAVES AND ALSO WATER CHANNNELS AND ALL THAT STUFF, IT USES THE SAME PRINCIPLE OF DOING GEOMETRY AT RIGHT ANGLES TO MAKE VARIABLE SHAPES. THE IMPORTANT THING TOO REMEBER IS THAT THE SHAPE ALTHOUGH ROUND OR CURVY IS MADE FROM A BASIC SHAPE A FRACTAL.  I PUT IT ON A SHEET OF PAPER BELOW IN BASIC FORM.

IF YOU LOOK AT THE DIAGRAM YOULL SEE THERE IS ONE MAIN BRACH THEN TWO THAT BREAKS DOWN AGAIN INTO SMALLER BRANCHES. THERES A BASIC RELATIONSHIP IN THAT MODEL OF A STRAIGHT LINE AT 90 DEGREES STRAIGHT UP THEN ONE AT 45 DEGREES AND THEN ANOTHER AT 90 DEGREES AGAIN. TWO 45 DEGREE ANGLES MAKING ONE RIGHT ANGLE ACROSS THE MAIN BRANCH. ANYWAY O PUT A VARIABLE AMOUNT OF GREEN BRANCHES AND LEAVES ON THE MODEL. PERHAPS YOU CAN SEE AS WE MOVE TOO THE END THE AMOUNT OF LITTLE GREEN LEAVES CHANGES TO GIVE THE BUSHEY APPEARANCE OF A TREE. ON A COMPUTER THAT IS EASY TO MODEL AND PROGRAM. AS A GENERAL RULE THE PROGRAM USES SINES AND COSINES (USE YOUR TABLES!) FROM THE COMPUTER ROM ITS USUALLY DENOTED BY SIN OR COS IN THE BASIC OR LANGUAGE YOUR USING. ITLL ALSO BE IN THE TABLES STORED IN THE COMPUTER IN THE HARDWARE AS RAW VALUES LIKE IN A SIN OR COSINE TABLE BOOK. IN THE HARDWARE THE MANUFACTURER MAY ONLY USE THE VALUES UP TOO 90 DEGREES TO SAVE SPACE EXPECTING THE PROGRAM OR BASIC INTERPRETER TO RECALCULATE THE NEXT QUADRANT ITSELF, IT JUST REALLY SUBTRACTS OR ADDS DEPENDING ON WHAT YOUR DOING REALLY. ANY WAY THE BASIC STUFF IS MAKE A STRAIGHT LINE DIVIDE IT IN HALF AND TURN ONE HALF THROUGH 90 DEGREES. YOU BASICALLY TURN THE LINE FROM THE POINT IN THE MIDDLE THRU AN ARC AS A RADIUS OF THE CIRCLE BUT YOU MUST KEEP IT AT 90 DEGREES. THE VALUE IS REALLY PRETTY EASY TO MAKE A CIRCLE OU MAP A SINE AND A COSINE TOGETHER SO IF YOU USE A PLOT OF PIXELS THOSE LITTLE DOTS YOU MIGHT USE SIN (A) WHERE A IS THE ANGLE, AND COSINE (A), THE ANGLE INCLUDED ON BOTH IS THE SAME FOR A CIRCLE. YOU CAN START ANYWHERE AROUND IT BUT JUST REMEBER TOO. YOU REALLY JUST MOVE ONE RADIUS AROUND IT. YOU WILL HAVE TOO USE ANOTHER DIRECTION FOR DEPTH ON A 3 DIMENSIONAL MODEL USUALLY WE ALL CALL IT Z SO ITS X,Y,Z. THE X AND Y ARE THE SAME AS A NORMAL GRAPH X ACROSS Y UP SO YOU USE Z GOING BACK FOR DEPTH. THERES A FEW EQUATIONS OR METHODS OF TURNING THE MODEL ILL DO THAT ON ANOTHE R PAGE.  PLEASE REMEMBER WHEN YOU PROGRAM ANYTHING ON A COMPUTER SCREEN MAY BE MAPPED WITH THE POINT X=0 Y=0 IN THE LEFT TOP CORNER INSTEAD SO YU HAVE TO MAVE IT TOO THEM MIDDLE. IT WILL END UP SOMETHING LIKE THIS FOR A CIRCLE.

X= S * SIN(A)+OFFSET

Y = S*(COS(A)+OFFSET

PLOY X,Y

THE X AND Y ARE THE CO-ORCINATES ON A STANDARD GRAPH WHERE ITS DIVIDED INTO 4 QUADRANTS NOTHING SINISTER. S IS THE SCALE WHERE YOU MULTIPLY THE SINE OR COSINE VALUE BY A LARGER VALUE JUST TOO MAKE IT BIGGER, OTHERWISE THE VALUES WILL BE TOO SMALL TOO SEE AND YOU WONT SEE ANYTHING EXCEPT A SMALL DOT AT THE TOP CORNER OR IN THE MIDDLE. YOU NEED THE IMAGE AT THE ORIGIN OF THE GRAPH, IN THIS MODEL( INCIDENTALLY WE CAN MOVE IT OR EVEN RECALCULATE IT FROM ANOTHER PROGRAM TO MOVE THE WHOLE IMAGE IN DATA LAYERS. YOU JUST ADD A VALUE TO THEM TO MOVE THEM UP AND DOWN THE SCREEN AND ACROSS THATS AN EASY WAY TO MOVE OBJECTS FROM A JOYSTICK. YOU JUST TAKE THE VALUE FROM THE STICK AND ADD A VALUE OR SUBTRACT IT WHILE THE PROGRAM MAKES THE IMAGE IN A LOOP SO IT REDRAWS IT AND MOVES. AS THE ONE ABOVE IS A QUICK DIAGRAM WELL DO THE SPINNING BACKWARDS AFTER. BUT TOO SPIN IT TOMMEE TIPPEEE STYLE HEAD OVER HEELS, MOVE ALL THE CO-ORDINATES ROUND THE CIRCLE. THATS WHY YOU HAVE TOO CALCULATE THE ANGLE AT A RIGHT ANGLE TO MODEL THE FRACTAL STUFF PROPERLY. IF THE POINT IS MOVING IN A SMALLER CIRCLE USE A SMALLER RADIUS, SO IT SPINS IN A SMALLER CIRCLE WITH ITS OWN ORIGIN IF NECCESARY. THEN YOU CAN MOVE THE IMAGE SPINNING ROUND A POINT OTHER THAN THE MIDDLE.  YOU JUST HAVE TOO THINK ABOUT WHAT YOU WANT AND THE BEST WAY (ALGORITHM) TOO DO IT!DOES THAT MATTER ? IT DOES IF YOURE A COMPUTER.  BUT WHAT MATTERS IS THAT IT DOES SHOW HOW STRUCTURES CAN BE BUILT FROM FRACTALS INTO A REAL 3D OBJECT. YOU CAN DO  FRACTAL FILLS WHERE YOU COVER AN ENCLOSED SHAPE WITH THEM BY MAKING THE RIGHT ANGLE COMPONENT BIGGER OR SMALLER TOO SCALE IT AND MOVING IT INTO THE GAPS SO YOU JUST FIT IT IN TILL THERES NO MORE ROOM. THATS JUST A SIMPLE WAY TO DO A FRACTAL FILL. ILL LEAVE THAT THERE. DONT WORRY IF IT LOOKS CONFUSING. THATS WHY NOBODY ELSE EVER TOLD YOU HOW TOO DO THIS!

UNDER CONSTRUCTION