Fractal 081 C – Drop
Part of ELEMENTS series – 05 2022
blue . drop . life . reflection . transparence . water


Fractal 081 C – zoom level 1

Fractal 081 C – zoom level 2
Data
This digital works is created exclusively from fractals, with 0% AI generated. It can therefore be converted into a set of functions and parameters that can be the basis for the training of an AI.
The mathematical formulas and parameter combinations corresponding to each fractal are presented below. In each case, the numerical characters have been replaced by â– to prevent unauthorized reproduction. If you are interested in using the full data set to train an AI, please contact Philippe.
Fractal 081 C - Drop - Part of ELEMENTS series - 05.2022
Fractal_â– â– â– _C { fractal: title="Fractal_â– â– â– _C" width=â– â– â– â– height=â– â– â– â– layers=â– credits="Philoxerax;â– /â– /â– â– â– â– " layer: caption="Layer â– " opacity=â– â– mergemode=addition mapping: center=-â– .â– â– â– â– â– â– â– â– â– â– â– â– â– /â– .â– â– â– â– â– â– â– â– â– â– â– â– â– magn=â– â– â– â– .â– â– angle=-â– â– â– .â– â– â– â– formula: maxiter=â– â– â– filename="lkmâ– .ufm" entry="mixed-up-multiplication-mandelbrot" p_power=â– p_bailout=â– â– â– â– p_shape_type=square p_qâ– _type=out p_qâ– _type=out p_qâ– _type=out p_qâ– _type=out p_freq=â– p_amp=â– .â– p_nteeth=â– p_rsmall=â– .â– p_inrad=â– .â– â– inside: transfer=none outside: transfer=linear gradient: smooth=yes rotation=â– â– index=â– â– color=â– index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– opacity: smooth=no index=â– opacity=â– â– â– layer: caption="Background" opacity=â– â– â– mergemode=overlay mapping: center=-â– .â– â– â– â– â– â– â– â– â– â– â– â– â– /â– .â– â– â– â– â– â– â– â– â– â– â– â– â– magn=â– â– â– â– .â– â– angle=-â– â– â– .â– â– â– â– formula: maxiter=â– â– â– filename="lkmâ– .ufm" entry="mixed-up-multiplication-mandelbrot" p_power=â– p_bailout=â– â– â– â– p_shape_type=square p_qâ– _type=out p_qâ– _type=out p_qâ– _type=out p_qâ– _type=out p_freq=â– p_amp=â– .â– p_nteeth=â– p_rsmall=â– .â– p_inrad=â– .â– â– inside: transfer=none outside: transfer=linear gradient: smooth=yes rotation=-â– â– index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â– index=-â– â– color=â– â– â– â– â– â– â– opacity: smooth=no index=â– opacity=â– â– â– layer: caption="Layer â– " opacity=â– â– â– mergemode=lighten mapping: center=-â– .â– â– â– â– â– â– â– â– â– â– â– â– /â– .â– â– â– â– â– â– â– â– â– â– â– â– magn=â– â– â– .â– â– â– â– â– angle=-â– â– â– â– .â– â– â– â– formula: maxiter=â– â– â– filename="mt.ufm" entry="mt-â– â– â– â– â– â– a-m" p_eâ– =â– .â– p_eâ– =â– .â– p_bailout=â– â– â– â– .â– f_fnâ– =flip f_fnâ– =ident inside: transfer=none outside: transfer=linear gradient: smooth=yes rotation=â– â– â– index=â– â– â– color=â– index=â– â– â– color=â– index=â– â– â– color=â– index=â– â– â– color=â– â– â– â– â– â– â– index=â– â– â– color=â– index=â– â– â– color=â– index=â– â– â– color=â– index=â– â– â– color=â– opacity: smooth=no index=â– opacity=â– â– â– layer: caption="Layer â– " opacity=â– â– mergemode=overlay mapping: center=-â– .â– â– â– â– â– â– â– â– â– â– â– â– /â– .â– â– â– â– â– â– â– â– â– â– â– â– magn=â– â– â– .â– â– â– â– â– angle=-â– â– â– â– .â– â– â– â– formula: maxiter=â– â– â– filename="mt.ufm" entry="mt-â– â– â– â– â– â– a-m" p_eâ– =â– .â– p_eâ– =â– .â– p_bailout=â– â– â– â– .â– f_fnâ– =flip f_fnâ– =ident inside: transfer=none solid=â– â– â– â– â– â– â– â– â– â– outside: transfer=linear gradient: smooth=yes rotation=â– â– index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– index=â– â– color=â– â– â– â– â– â– â– â– index=â– â– color=â– â– â– â– â– â– â– â– index=â– â– color=â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â– opacity: smooth=no index=â– opacity=â– â– â– layer: caption="Layer â– " opacity=â– â– â– mapping: center=-â– .â– â– â– â– â– â– â– â– â– â– â– â– /â– .â– â– â– â– â– â– â– â– â– â– â– â– magn=â– â– â– .â– â– â– â– â– angle=-â– â– â– â– .â– â– â– â– formula: maxiter=â– â– â– filename="mt.ufm" entry="mt-â– â– â– â– â– â– a-m" p_eâ– =â– .â– p_eâ– =â– .â– p_bailout=â– â– â– â– .â– f_fnâ– =flip f_fnâ– =ident inside: transfer=none solid=â– â– â– â– â– â– â– â– â– â– outside: transfer=linear gradient: smooth=yes rotation=â– â– index=â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– index=â– â– color=â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– index=â– â– â– color=â– â– â– â– â– â– â– â– index=â– â– â– color=â– opacity: smooth=no index=â– opacity=â– â– â– } mixed-up-multiplication-mandelbrot { ; Kerry Mitchell â– â– Novâ– â– â– â– ; ; Instead of using regular complex multiplication, this method uses a base ; shape (= unit circle normally). Use the polar angle of z to reach back ; to the base shape and find its coordinates. Then, use the actual and base ; magnitudes to determine a scale factor, and the arc length to determine ; the angle (angle = arc length / base magnitude). From there, the magnitude ; of z^power = scale factor ^ power, and angle of z^power = power â– angle. ; $define debug global: complex corner[â– â– ] float pitch_s=â– float pitch_trad=â– float smax=â– float tdegmax[â– â– ] float twopi=â– â– #pi int gi=â– ; ; cruciform settings: central square side & four other squares, one ; on each side of central square ; if(@shape_type=="cruciform") corner[â– ]=(â– ,â– ) corner[â– ]=(â– ,â– ) corner[â– ]=(â– ,â– ) corner[â– ]=(â– ,â– ) corner[â– ]=(-â– ,â– ) corner[â– ]=(-â– ,â– ) corner[â– ]=(-â– ,â– ) corner[â– ]=(-â– ,-â– ) corner[â– ]=(-â– ,-â– ) corner[â– ]=(-â– ,-â– ) corner[â– â– ]=(â– ,-â– ) corner[â– â– ]=(â– ,-â– ) corner[â– â– ]=(â– ,-â– ) corner[â– â– ]=(â– ,â– ) ; ; rescale so that corner[â– ] = (â– ,â– ) ; find degree measures of corners ; gi=-â– while(gi<â– â– ) gi=gi+â– corner[gi]=corner[gi]/â– tdegmax[gi]=(atanâ– (corner[gi])/#piâ– â– â– â– +â– â– â– )%â– â– â– endwhile elseif(@shape_type=="triangle") corner[â– ]=(â– ,â– ) corner[â– ]=(-â– +flip(sqrt(â– )))/â– corner[â– ]=(-â– -flip(sqrt(â– )))/â– tdegmax[â– ]=â– tdegmax[â– ]=â– â– â– tdegmax[â– ]=â– â– â– tdegmax[â– ]=â– â– â– elseif(@shape_type=="star") corner[â– ]=(â– ,â– ) corner[â– ]=@inradâ– (â– ,â– )/sqrt(â– ) corner[â– ]=(â– ,â– ) corner[â– ]=@inradâ– (-â– ,â– )/sqrt(â– ) corner[â– ]=(-â– ,â– ) corner[â– ]=@inradâ– (-â– ,-â– )/sqrt(â– ) corner[â– ]=(â– ,-â– ) corner[â– ]=@inradâ– (â– ,-â– )/sqrt(â– ) corner[â– ]=(â– ,â– ) tdegmax[â– ]=â– tdegmax[â– ]=â– â– tdegmax[â– ]=â– â– tdegmax[â– ]=â– â– â– tdegmax[â– ]=â– â– â– tdegmax[â– ]=â– â– â– tdegmax[â– ]=â– â– â– tdegmax[â– ]=â– â– â– tdegmax[â– ]=â– â– â– endif ; ; gear settings ; if(@shape_type=="gear") pitch_trad=twopi/@nteeth smax=#piâ– (â– +@rsmall) pitch_s=smax/@nteeth endif init: complex arccenter=(â– ,â– ) complex c=#pixel complex compk=(â– ,â– ) complex w=(â– ,â– ) complex z=#pixel float afac=â– float bfac=â– float cfac=â– float dcrit=â– /(â– +@rsmall) float dtooth=â– float hâ– =â– float kâ– =â– float k=â– float phi=â– float phimax=â– float r=â– float s=â– float slope=â– float tdeg=â– float third=â– /â– float trad=â– float x=â– float xb=â– float xâ– =â– float y=â– float yb=â– float yâ– =â– int itooth=â– loop: ; ; decompose z ; x=real(z), y=imag(z) ; ; square ; if(@shape_type=="square") ; ; determine arc length from basis shape ; phimax=â– ; ; find scale factor k ; k=abs(x) if(abs(y)>k) k=abs(y) endif ; ; find standard polar angle ; trad=atanâ– (z) if(trad<â– ) trad=trad+â– â– #pi endif tdeg=trad/#piâ– â– â– â– ; ; use polar angle to find coordinates of point on base shape ; and base shape arc length ; if(tdeg<â– â– ) ; upper right side xb=â– , yb=y/k, s=yb elseif(tdeg<â– â– â– ) ; top xb=x/k, yb=â– , s=â– -xb elseif(tdeg<â– â– â– ) ; left side xb=-â– , yb=y/k, s=â– -yb elseif(tdeg<â– â– â– ) ; bottom xb=x/k, yb=-â– , s=â– +xb else ; lower right side xb=â– , yb=y/k, s=â– +yb endif phi=s ; ; raise z to power ; k=k^@power, phi=(@powerâ– phi)%phimax ; ; use phi and k to return new x & y and add c ; if(phi<â– ) ; upper right side xb=â– , yb=phi elseif(phi<â– ) ; top xb=â– -phi, yb=â– elseif(phi<â– ) ; left side xb=-â– , yb=â– -phi elseif(phi<â– ) ; bottom xb=phi-â– , yb=-â– else ; lower right side xb=â– , yb=phi-â– endif x=xbâ– k, y=ybâ– k z=x+flip(y)+c ; ; triangle ; elseif(@shape_type=="triangle") ; ; determine arc length from basis shape ; third=sqrt(â– ) phimax=â– â– third ; ; find standard magnitude and polar angle ; r=cabs(z) trad=atanâ– (z) tdeg=(trad/#piâ– â– â– â– +â– â– â– )%â– â– â– trad=tdeg/â– â– â– â– #pi ; ; use polar angle to find coordinates of point on base shape ; and base shape arc length ; if(tdeg
